Design of a novel crack-free precipitation-strengthened nickel-based superalloy and composites for laser powder bed fusion

ABSTRACT Avoiding cracking defects is crucial to ensuring processability in the laser powder bed fusion (LPBF) of metallic materials. In this study, a crack-free Ni-based superalloy with a high volume fraction of the γ′ phase was designed for the LPBF process using the thermodynamic approach. The results indicate that the designed SD01 Ni-based alloy was crack-free and over 21% of the spherical γ′ phase was uniformly distributed in the matrix after heat treatment. In addition, 1 wt.% TiB2 particles were introduced into the SD01 alloy to further enhance high-temperature mechanical performance. It was found that the morphology of the γ′ phase was altered from spherical to cubic structures, and its volume fraction increased from 21% to 40% after the TiB2 addition. The SD01-TiB2 composite exhibited an excellent combination of tensile strength (437.43 MPa) and elongation (7.71%) at 900 °C compared with the SD01 alloy (252.03 MPa, 3.02%). These findings provide a new metallic material design method for the LPBF of crack-free high-performance Ni-based materials.

P u blis h e r s p a g e : h t t p:// dx. d oi.o r g/ 1 0. 1 0 8 0/ 1 7 4 5 2 7 5 9. 2 0 2 3. 2 2 2 4 7 6 9 Pl e a s e n o t e: C h a n g e s m a d e a s a r e s ul t of p u blis hi n g p r o c e s s e s s u c h a s c o py-e di ti n g, fo r m a t ti n g a n d p a g e n u m b e r s m a y n o t b e r efl e c t e d in t hi s v e r sio n. Fo r t h e d efi nitiv e v e r sio n of t hi s p u blic a tio n, pl e a s e r ef e r

t o t h e p u blis h e d s o u r c e . You a r e a d vis e d t o c o n s ul t t h e p u blis h e r's v e r sio n if yo u wis h t o ci t e t hi s p a p er.
This ve r sio n is b ei n g m a d e a v ail a bl e in a c c o r d a n c e wi t h p u blis h e r p olici e s. S e e h t t p://o r c a . cf. a c. u k/ p olici e s. h t ml fo r u s a g e p olici e s. Co py ri g h t a n d m o r al ri g h t s fo r p u blic a tio n s m a d e a v ail a bl e in ORCA a r e r e t ai n e d by t h e c o py ri g h t h ol d e r s .

Introduction
Nickel-based superalloys have been extensively used in the aviation, aerospace and transportation fields because of their remarkable tensile strength, creep properties and superior oxidation resistance under elevated temperature conditions (Fan et al. 2021;Grilli et al. 2017;Tan et al. 2020). For instance, the turbine discs and blades made of Ni-based superalloys typically operate at temperatures exceeding 900°C (Furrer and Fecht 1999;Singh 2014). Traditionally, Ni-based superalloys were manufactured mainly by casting, forging and powder metallurgy methods, but these were limited by their high-costs, long lead times and geometric constraints (Reed 2008;Selvaraj et al. 2021). Recent advances in laser powder bed fusion (LPBF) have provided a new method for the fabrication of Ni-based superalloys (Haines et al. 2022;Liu et al. 2022). The LPBF process could form complex structural parts with its natural digital characteristics, thus simplifying the manufacturing process and shortening the manufacturing chain (Narasimharaju et al. 2022). Nevertheless, Nibased superalloys are sensitive to cracking, which is highly related to their rapid cooling rates, spatially variable temperature gradients and intrinsic thermal cycling induced by the LPBF process (Guo et al. 2023;Tang et al. 2021;Zhao et al. 2023). These non-uniform cooling rates and large thermal gradients typically generate high levels of residual stress in additively manufactured materials, inducing the formation of micro-cracks and delamination. Recent studies (Tang et al. 2021;Yu et al. 2022) have highlighted the following modes of crack formation in the LPBF of Ni-based superalloys: Solid-state cracking. Solid-state cracks are induced by residual stress from precipitation (γ ′ phase), resulting in a strain exceeding the limited ductility of the matrix . Solid-state cracks are characterised by parallel straight sides, generally showing a sharp kink close to 90°but without the presence of dendrite arms or liquid film traces.
Liquation cracking. Liquation cracks are generated in the thermal cycle stage, which is inherent in the LPBF process. Some low-melting precipitates are re-heated multiple times and melted as the laser heats up to a nearby area. The liquid phase acts as a crack initiation point for the influence of residual stress (Tang et al. 2021;Zhou et al. 2022). Eutectic phases with low melting points generally precipitate around the liquation cracks.
Solidification cracking. These cracks occur in the solidification stage of the LPBF process. Dendrite arms and liquid films are along the cracks, indicating that the cracks initiate from the residual liquid between dendrite arms and that insufficient feeding is provided by the residual liquid to accommodate the solidification shrinkage strain (Tang et al. 2021).
Recently, the addition of ceramic particles has proven to be a feasible approach for eliminating cracks and improving the tensile strength of solid-solution-strengthened Ni-based superalloys. For instance, Zhang et al. added 1wt.% TiB 2 particles into GH3230 to eliminate cracks and achieve better strength and elongation than pure GH3230 ; Han et al. found that TiC nanoparticles played a positive role in cracking elimination and tensile performance enhancement of LPBFfabricated Hastelloy X (HX) nanocomposites (Han et al. 2020). Meanwhile, TiB 2 ,Y 2 O 3 and WC particles were also introduced into HX to fabricate high-strength and defect-free HX composites (Cheng et al. 2021;H a ne ta l . 2021;Y a n ge ta l .2021). Notably, the above researchers all reported that the addition of reinforcing particles could inhibit the initiation and propagation of cracks, reducing the fraction of the defects and improving mechanical properties. Nevertheless, it is still a challenge for these composites to meet strength requirements under elevated temperature conditions, mainly because of their relatively weak matrix materials.
Compared with the solid-solution-strengthened Nibased alloys, precipitation-strengthened Ni-based alloys exhibit outstanding high-temperature strength because of the enhancement of the γ ′ phase (Takahashi, Kawanabe, and Ghoniem 2010). However, the precipitation of the γ' phase also increases the generation of residual stress, which in turn increases cracking susceptibility . Lv et al. proposed a method to decrease the cracking susceptibility of CM247LC superalloy by adding nanoscale TiC particles. The results showed that the fraction of cracks in CM247LC alloy could be reduced but not eliminated (Lv et al. 2022). This finding indicated that the addition of nucleation agents is not an effective approach to heal cracking within the LPBF of precipitation Ni-based alloys, although it has been proven feasible in the elimination of hot cracking during the LPBF of solid-solutionstrengthened nickel alloys .
One of the feasible solutions to the LPBF of Ni-based superalloys is to optimise the contents of the Al, Ti, Nb and Ta elements in order to achieve proper LPBF processability while maintaining the volume fraction of the γ ′ phase. Tang et al. designed two novel crack-free superalloys, named ABD-850AM and ABD-900AM, by calculating crack susceptibility and avoiding defect formation using thermodynamic simulations (Tang et al. 2021). The properties of the alloys, however, were found to be reduced because of the loss of γ' phase volume fraction, although the cracks were eliminated by changing the element content. Ji-Un Park et al. used the René 80 composition as a baseline to obtain a crack-free selective electron beam melting superalloy (AM80) with a high γ ′ volume fraction by reducing Ti (5→3 wt. %) but adding 2.5 wt. % Ta and 1.0 wt. % Hf (Park et al. 2022). The designed AM80 alloy exhibited superior tensile properties (805 ± 6 MPa) at 870°C without any cracks being formed. Zhu et al. investigated the effect of Nb and Ta in a Ni-Co-based superalloy, showing that the alloying effects of Nb and Ta on γ ′ phase could strengthen stability (Zhu et al. 2023). Therefore, increasing Nb and Ta elements is highly recommended to improve mechanical performance in next-generation Ni-based superalloys. Nonetheless, designing a perfect Ni-based superalloy with excellent high-temperature properties is difficult because of γ ′ redissolution into the matrix at high temperatures.
In this study, thermodynamic calculations were performed to design a crack-free Ni-based superalloy for the LPBF process by considering the solidification crack index (SCI), the freezing range (FR) and the strain-age crack (SAC) index while maintaining a high volume fraction of the γ ′ phase. Response surface methodology (RSM) was applied to optimise the Ni-based superalloy (SD01) by fully considering cracking susceptibility and the γ' phase fraction. The influence of TiB 2 addition and heat treatment (HT) on microstructures, precipitation and mechanical properties was also discussed. The various possible strengthening mechanisms of the SD01 and SD01 composite (SD01-C) were also described in this study.

The alloy design methodology
The mechanical behaviour of precipitation-strengthened Ni-based alloys fabricated with the LPBF process is influenced by various factors, including cracking susceptibility, γ ′ phase properties (volume fraction, size and shape) and LPBF process parameters (Sanchez et al. 2021;Shahwaz, Nath, and Sen 2022). Cracking susceptibility and γ ′ phase volume fraction were chosen in this study as the primary considerations for the alloy design. The SCI, FR and SAC indicators were used to measure the cracking susceptibility using the following equations (Kou 2015;Tang et al. 2021): where f s is the solid fraction. The SCI value is the average value when the value range of solid fraction is between 0.9 and 0.99. A high SCI value indicates a slow growth rate of columnar grains, meaning that the liquid channel of neighbouring columnar grains is difficult to fill, leading a long sharp notch to promote crack initiation (Chauvet et al. 2018).
where T Liquidus is the liquidus temperature and T Solidus is the solidus temperature. A wide freezing range generally indicates a high crack susceptibility (Dupont, Lippold, and Kiser 2011).
where V g f is the volume fraction of γ phase, and T * g is the critical temperature of 0.7T solidus . A high SAC value indicates a high crack sensitivity brought by the volume change of precipitations (Yu et al. 2022b).
These data were calculated with Thermo-Calc software with the TCNI9 database by using the Scheil-Gulliver solidification module and the equilibrium solidification module, with a temperature step size of 1 K. The weight fractions of Al, Ti, Nb, and Ta were selected as significant indicators because they were the main components for the γ' phase, and they played an important role in reducing cracking susceptibility. The optimum alloy composition was determined using RSM, which allowed for the multi-objective optimisation of various index trade-offs (Şimşek, Tansel İç, and Şimşek 2016).
A total of 30 element combinations were carried out in this study, and the ranges of the volume fractions of Al, Ti, Nb and Ta were selected based on the ABD-850AM reference alloy (Tang et al. 2021). Table 1 shows the experimental codes and factors.
The alloy design approach aims to increase LPBF processability while maintaining the high-temperature strength of the superalloy by holding a high γ' volume fraction. The increase in γ' phase fraction has a strong positive correlation with the addition of Al, Ti, Nb and Ta, which, in turn, increases cracking susceptibility (Henderson et al. 2004). Therefore, the cracking susceptibility and γ' volume fraction were the two primary factors for optimisation in this study. The optimisation could be formulated in the standard mathematical format as follows: Find: Minimise: Maximise: Within the following ranges: where ω Al , ω Ti , ω Nb and ω Ta are the weight fractions of Al, Ti, Nb and Ta, respectively.
Afterward, a total of 30 variants were set to determine four regression models (R SAC ,R SCI ,R FR and R γ' ) between the four elements and four dependent variables by regression fitting, according to the central composite design method. The equations are as follows:

Regression Equations
R FR (K) =−33.1Al − 78.1Ti + 86.1Nb + 92.5Ta where (Al), (Ti), (Nb), and (Ta) are the weight fractions of the four elements, respectively. The candidate compositions were screened based on the lowest cracking susceptibility and the highest γ' volume fraction within the design ranges.

The feedstock
In this study, the designed SD01 spherical powder was produced by Avimetal Powder Metallurgy Technology (Beijing, China) and the sub-micrometre TiB 2 powder was supplied by CWnano (Shanghai, China). To produce the SD01 spherical powder, the alloy ingot was obtained using vacuum melting according to the designed composition of the SD01 alloy, followed by argon atomisation. A high-speed mixer (SpeedMixer DAC 800.1 FVZ, Nordrhein-Westfalen, Germany) was used to prepare the composite feedstock. During the mixing procedure, the weight ratio of SD01 and TiB 2 was set to 99:1. The experiments were carried out at a mixing speed of 1,200 rpm and a mixing time of 1.5 min, followed by cooling to room temperature (RT). This process was repeated three times.

The LPBF process and heat treatment
The LPBF process was carried out in a 100 × 100 × 200 mm 3 build volume under argon atmosphere protection using a Concept Laser Mlab cusing 200R (GE, Lichtenfels, Germany) equipped with a modulated 200 W ytterbium fibre laser (wavelength = 1,070 nm). The laser scanning speed and hatch spacing parameters were optimised to obtain high-density specimens, while the laser power was fixed at 190 W, and the powder thickness was set to 40 μm. The island scanning strategy with 67°rotation between subsequent layers was used to minimise porosity ( Figure 1e). Cubic specimens with dimensions of 7 × 7 × 8 mm 3 were fabricated to optimise the process parameters and analyse microstructural evolution.
To explore the effects of HT on the microstructure and mechanical properties, a sintering furnace (SX-G20133, China) protected by argon cover gas flowing was used. The equilibrium solidification phase diagram was calculated using JMatPro 7.0 software (Sente Software Ltd, UK) with the TTNi8 database. Figure 1a shows that the HT strategy consisted of two parts: the solution treatment and the ageing treatment. All as-fabricated (AB) specimens were heated to temperature T 1 for 2 h, followed by air cooling to homogenise the microstructure and dissolve the harmful phases in the AB specimens (Harte et al. 2020). The ageing treatment was performed at T 2 for 16 h to precipitate the γ' phase. Solution temperature T 1 and ageing temperature T 2 were determined using the equilibrium solidification phase diagram (Figure 1b). To isolate the effect of TiB 2 on strength improvement, all specimens were heat treated under the same conditions (1050°C /2 h + 750°C /16 h), followed by air cooling.

Mechanical and microstructural characterisation
As Figure 1c shows, the tensile specimens were horizontally sectioned perpendicular to the build direction from both the as-fabricated and heat-treated plates with a dimension of 70 × 30 × 2.5 mm (length x width x thickness). The dimensions of the tensile specimens are shown in Figure 1d. The tensile tests were performed at RT using a microcomputer-controlled electronic universal testing machine (FBS-100KNW, FBS, Shenzhen, China) with a constant extension rate of 0.03 min −1 . The QJ212 (Shanghai, China) uniaxial tensile testing system was used to perform elevated-temperature (900°C and 1,000°C) tensile testing with strain rates of 0.014 and 0.07 min −1 before and after the yield stage, respectively. The microstructure was examined using an optical microscope and a field-emission scanning electron microscope. Grain orientation and grain boundary distribution were analysed using electron backscatter diffraction (EBSD) with a step of 1 μm. An X-ray diffraction (XRD) instrument (Smart Lab 3 kW, Japan) equipped with Cu-Kα radiation was used to detect the phase composition in the 2θ range of 30°-100°, with a step size of 3°.

The designed alloy composition and feedstock
The 3D graphs of the R SCI response surface were built from a regression model to minimise the SCI indicator ( Figure 2). The purple-coloured portion of the graph indicates lower SCI values. When only 2 chemical components are graphed for 3D response plots in Figures  2 and 3, the other chemical components' values are fixed at the middle values of the original range (Table  1). The surface shows that a reduction in Al contributed the most to the reduction in SCI value; the minimum values were 1280, 950, and 870 from the Figure 2a, c and e, respectively, and the content of Al was minimum during this time (1.2%). However, the interaction of Al and Ti 2 played a significant effect on the SCI when the Ti content was lower or higher than 2.30% and two peaks were generated ( Figure 2a). Figure 2b and d show that the contribution of Ti was second only to the contribution of Al and that increasing the Ti content reduced the SCI when the Al content was fixed at 1.7%. Furthermore, the combination of increasing Ta and decreasing Nb was found to reduce the SCI value, as shown in Figure 2f. Based on the simulation, the optimum combination of Al, Ti, Nb and Ta to achieve a minimum SCI was 1.2%, 2.3%, 1.1% and 0.6%, respectively. Figure 3 shows the surface diagrams of the FR depending on the fractions of Al, Ti, Nb and Ta. It was found that the Al and Ta contents affected the FR indicator more than did the Ti and Nb contents. Furthermore, the FR value decreased with a decrease in the Al content. The surface diagrams show that increasing Ta significantly enhanced the FR value. It should be noted that the combination of Al 1.2%, Ti 2.5%, Nb 1.8% and Ta 0.6% was optimal in decreasing the FR value.
Generally, the volume fraction of the γ' phase increased with an increase in the Al, Ti, Nb and Ta elements, whereas the SAC presented an opposite tendency compared to the increase in the γ' phase based on the simulation obtained in Equations 9 and 10. In this study, a multi-objective optimisation (Equations 4-6) was carried out using a desirability function to optimise the contents of Al, Ti, Nb and Ta in terms of minimising the SCI, FR and SAC indicators while maximising the value of the γ' phase volume fraction at 900°C. The solution with the highest desirability among 97 solutions suggested by the regression models (Equations 7-10) was selected as our optimal solution. The chosen solution showed that the secondorder RSM regression models predicted that the value of the γ' phase volume fraction at 900°C, the SCI, the SAC and the FR were optimal when the values of the material composition parameters were 1.94% Al, 2.4% Ti, 1.5% Nb and 1.25% Ta. The chemical composition of the designed Ni-based alloy (SD01) and the atomised powder are presented in Table 2. Figure 4a and b show the morphologies of the spherical SD01 powder and the irregular-shaped TiB 2 powder, respectively. The particle distributions of spherical SD01 powder were examined at D10 = 19.35 μm, D50 = 33.85 μm, and D90 = 55.52 μm, while the irregular-shaped TiB 2 powder had a mean size of 500 nm. The schematic diagram of the planetary mixture is shown in Figure 4e. After the high-speed mixture, the TiB 2 powder uniformly adhered to the SD01 surface, and no apparent clusters were formed (Figure 4c-d). The XRD spectra of the TiB 2 submicron particles, SD01 raw powders and SD01 composite (SD01-C) powders are shown in Figure 4f. Note that the addition of 1 wt.% TiB 2 submicron particles and the planetary powder mixture process did not influence the main diffraction peak of SD01. Furthermore, Figure 4g shows the TiB 2 peaks in the SD01-C powder, suggesting that the TiB 2 submicron particles remained stable in the composite powder during the entire mixture process.   solidification (F s = 0.9 -F s = 0.99 ) was considered the crucial period for crack initiation. A higher FR (F s = 0.9 -F s = 0.99 ) value implied that the incomplete bridging grain may cause residual liquid to remain on the boundaries, further causing hot cracking as a result of the residual stresses generated during the rapid cooling. As shown in Figure 5b, the critical FR (F s = 0.9 -F s = 0.99 ) values of  5c and d reveal that SD01 exhibited a lower SCI (F s = 0.9 -F s = 0.99 ) value (∼2,212.8 K) compared to IN738LC (∼3,673.2 K), but this value was slightly higher than the ABD-850 (∼2,173.8 K). A lower SCI value generally presented a stronger resistance to hot cracking during LPBF process (Tang et al. 2021), suggesting that the SD01 might exhibit similar LPBF processability with ABD-850 but much better than the IN738LC. Soild-state cracking was typically attributed to the residual stresses induced by solidification shrinkage coupled with the formation of the γ' phase during HT ; γ matrix ductility became most vulnerable at 0.5-0.8 T solidus (Singh and Andersson 2018). Generally, the increase in the fraction of the γ' phase resulted in an increase in the risk of solid-state cracking. Figure 5e and f show the variation of the γ matrix fraction and the γ' phase fraction, respectively, with regard to temperature. Note that the γ' phase volume fraction of SD01 was lower than that of IN738LC but higher than that of ABD-850 within the entire temperature range, implying that solid-state cracking may occur during the LPBF of SD01 under the non-optimal LPBF conditions, a topic which is further investigated in the next section.

Microstructure of the as-fabricated specimens
The microstructures of the SD01 and SD01-C under the scanning electron microscope (SEM) inspection are shown in Figure 6. The SD01 (Figure 6a-b) and SD01-C (Figure 6d-e) were mainly characterised by cellular structures, while TiB 2 addition promoted sub-grain boundary formation, as smaller cellular structures were formed in SD01-C. A number of white particles were found in the sub-grain boundaries and cells from SD01 (Figure 6b). The energy dispersive spectrometry (EDS) analysis of the particles and the matrix of SD01 is shown in Figure  6c, which demonstrates the higher contents of Ti, Nb, Mo and Ta in the particles, indicating that they are MC-type carbonitrides; this finding shows agreement with the literature (Donachie and Donachie 2002). In addition, based on the Scheil non-equilibrium simulation, the SD01 alloy may have a 0.4% mole volume fraction of carbonitride and a 3.3% mole volume fraction of Ni 3 Ti in the LPBF as-fabricated specimen. The EDS analysis of SD01-C in Figure 6f suggests that the white particles were mainly rich in Al, Ti, Nb, Mo and Ta elements. It is worth noting that the Al element was precipitated from the γ phase, indicating that the addition of TiB 2 promoted the precipitation of the main components of γ', which may have affected the mechanical performance of the SD01-C composite. Figure 7 shows the crystal orientation, grain morphology and grain boundary of the SD01 and SD01-C based on the EBSD inspection. Most of the grains in SD01 exhibited typical columnar structures parallel to the build direction (Figure 7a). The grains of SD01-C were more refined, and the average equivalent grain size was 7.84 μm, which was smaller than that of SD01 (10.35 μm), implying the grain refinement induced by the addition of 1 wt.% TiB 2 . The low maximum multiple of the uniform density of the SD01 and SD01-C in the pole figure (PF) maps were determined to be 13.85 and 9.23, respectively, indicating that TiB 2 addition also contributed to weakening the grain texture (Deng et al. 2018). The aspect ratio (AR) obtained from the inverse pole figure (IPF) orientation diagram is shown in Figure  7g. The total grain numbers of SD01 and SD01-C in the IPF region were found to 1,236 and 4,336, respectively, confirming that TiB 2 addition had a significant effect on grain refinement. In the range of 1-4 AR, the frequency of SD01 (3936) was higher than that of SD01-C (880). The frequencies of SD01 and SD01-C in the range of 4-8 AR were 243 and 371, respectively. Grain refinement could promote significant transformations of the grain boundary (Figure 7c and f). The fraction of high-angle grain boundaries (HAGBs) in the SD01 was 39.92%, while the value increased to 70.74% in the SD01-C. In general, HAGBs contain more dislocations (Tan et al. 2022b;Yang et al. 2021), and this might be caused by the introduction of TiB 2 particles. The increased dislocations and fine grains might have a significant impact on the mechanical performance improvement of the composite, which will be studied in the next section. Figure 8a and d show that the sub-grain boundaries were dissolved compared to the as-fabricated specimens (Figure 6a), which were replaced by many netstructured spherical γ' particles. The EDS results ( Figure  8e) show that the contents of Al, Ti, Nb and Ta in the precipitated phase were higher than those in the matrix, suggesting that the spherical precipitates were γ ′ phase. Previous studies (Reed 2006) have proven that the γ ′ phase is a FCC-like L1 2 ordered phase of composition Ni 3 X, where X is Al, while Ti, Nb and Ta could replace the Al in γ ′ phase (Jena and Chaturvedi 1984;Tang et al. 2021). Also, the spherical precipitate morphology is a typical feature of γ ′ phase in nickel-based superalloys (Haines et al. 2022;Reed 2006). Generally, a spherical morphology of γ ′ precipitates indicates a near-zero γ-γ ′ lattice misfit (Yoo 2005). It is worth noting that the precipitates were spatially aligned along the network of ablated sub-grain boundaries, suggesting that elastic energy played a significant role in controlling the microstructure and that γ ′ phase nucleation sites would preferentially appear at grain boundaries (Seitz and De Fontaine 1978;Su and Voorhees 1996). Figure 8b presents the SEM image of SD01-C after HT, in which sub-grain boundaries disappeared, but the morphology of the precipitated phase was cubic in shape and irregular. Compared to the γ matrix, the EDS analysis indicates that the Al, Ti, Nb, Ta contents were higher in the cubic precipitates (Figure 8c/e), especially Nb and Ta, while the Cr, Mo and W contents were higher in the irregular precipitates, which might be related to the precipitation of M 23 C 6 . Moreover, the γ' precipitates were formed and examined at the grain boundaries as well as within the grains in SD01-C, suggesting that the addition of TiB 2 may provide intragranular nucleation sites.

Characteristics of phase transformation after heat treatment
The fraction and average size of the γ ′ phase were calculated using the ImageJ Software. The γ ′ phase fractions of SD01 and SD01-C were 21% and 40.2%, respectively. The spherical γ ′ phase was 166 nm in diameter and the average length of the cubic and irregular precipitates was 332 nm. The SEM images showed the γ ′ particles with spherical shapes in SD01, while TiB 2 addition promoted M 23 C 6 precipitation and irregularity of the cubic γ ′ phase. Figure 8g and h show the IPF maps of the SD01 and SD01 -C. After HT, the average grain sizes of SD01 and SD01-C increased by 44% and 17%, respectively, indicating that TiB 2 addition could hinder the growth of grains during HT. Moreover, the fraction of low-angle grain boundaries in the SD01 increased from 60.08% to 63.85% after HT (Figure 7c/f), while the value in the SD01-C increased from 29.26% to 32.78% after HT (Figure 8f/i), suggesting that low-angle grain boundaries could make grain boundaries more tortuous, leading to the grains slip difficulties (Birosca, Gioacchino, and Stekovic 2014;Wei et al. 2021). Figure 9 shows the kernel average misorientation (KAM) maps of SD01 and SD01-C, offering a qualitative indication of the degree of plastic deformation of these specimens (Brewer, Field, and Merriman 2009). The average KAM values of SD01-AB and SD01-HT were calculated to be 0.55°and 0.54°, while the average KAM values of SD01-C-AB and SD01-C-HT were calculated to be 0.59°and 0.57°, indicating a reduction in the plastic deformation regions within the material due to the release of residual stress after HT. The dislocation densities of the four specimens were calculated using the KAM data via the formula (Wong, Hadadzadeh, and Wells 2018): KAMav is the average KAM value, μ is the step of EBSD (1 μm in this work) and b is the Burgers vector (0.25 nm in Ni-based superalloys (Konijnenberg, Zaefferer, and Raabe 2015;). The geometrically necessary dislocation density of the four specimens were 7.65 × 10 13 m −2 (SD01-AB), 7.56 × 10 13 m −2 (SD01-HT), 8.26 × 10 13 m −2 (SD01-C-AB) and 7.89 × 10 13 m −2 (SD01-C-HT), respectively.

Mechanical properties
The engineering stress-strain curves for the SD01 and SD01-C at RT, 900°C and 1000°C are shown in Figure 10a-c, respectively. The ultimate tensile strength (UTS) of the SD01-AB at RT was determined to be 954.31 ± 19.03 MPa and its elongation was 29.98 ± 1.14% (Figure 10a). In comparison, the SD01-HT was found to possess an ultrahigh UTS (1505.17 ± 34.39 MPa), and its elongation reached 20.08 ± 1.02% because of the precipitation of the γ ′ phase. Moreover, the UTS values of SD01-C-AB and SD01-C-HT at RT are 1117.15 ± 36.72 MPa and 1327.75 ± 53.05 MPa, respectively (Figure 10a). Compared to the SD01, the UTS values of SD01-C-AB was improved by 14.58%, while the UTS values of SD01-C-HT was reduced by 13.36%. The elongation of SD01-C-AB and SD01-C-HT decreased because of the formation of brittle phases, such as the γ ′ phase, M 23 C 6 and the added TiB 2 particles. It is worth noting that the yield strength values of SD01-C-AB and SD01-C-HT were 883.76 ± 29.04 MPa and 1244.97 ± 49.74 MPa, respectively, which were 16.75% and 6.7% higher than SD01-AB (883.76 ± 29.04 MPa) and SD01-HT (883.76 ± 29.04 MPa). The results indicate that adding TiB 2 particles offer a beneficial effect on the yield strength of the designed SD01 alloy under room-temperature condition.
The UTS values of the SD01-C and SD01 at 900°C were found to be 593.45 and 328.82 MPa, respectively ( Figure  10b). After HT, the UTS and elongation of SD01-C were found to drop to 469.06 MPa and 7.71%, respectively, because of the dissolution of dislocations, while the UTS of the SD01 also dropped to 315.04 MPa, but elongation increased to 3.02%. In addition, the SD01-C exhibited a notable improvement in strength and elongation at 1,000°C. The UTS of the SD01-C-AB at 1,000°C was significantly enhanced to 242.2 MPa, showing a significant improvement compared with the SD01-C-HT. However, the improvement was not obvious between SD01-AB and SD01-HT at 1,000°C, indicating that the majority of the γ ′ phase in SD01 might be dissolved into the matrix under the 1,000°C condition.
The mechanical properties of the designed Ni-based superalloy and composite were compared with those of a wide range of typical Ni-based superalloys processed by LPBF, as summarised in Figure 10d. Among the superalloys, SD01 achieved the highest strength at RT, whereas among many ceramic-reinforced alloys, SD01-C achieved the highest strength at 900°C. This finding indicates that the addition of 1 wt.% TiB 2 was more beneficial in improving the elevated temperature strengths of the materials. Figures 11 and 12 show the varying fracture morphologies of the different specimens after HT. The SD01 fracture at RT was ductile filled with dimples and accompanied by secondary cracks (Figure 11a). Many tearing steps were formed on the fractured surface of SD01 at an elevated temperature (Figure 11b and c), and the surface featured a flat breaking plane, although the fractured surface was coated with oxide layers (Figure 11b and c); this indicated that the fracture form was brittle. During elevated-temperature stretching, thermal stress promoted SD01 grain boundary oxidation and embrittlement, resulting in tearing steps (Fang et al. 2022). In the fracture morphologies (Figure 12a) of SD01-C, both dimples and tear features were formed and inspected, and they showed a ductile-brittle integrated fracture. Compared with those of SD01, the tearing steps of SD01-C decreased at elevated temperatures, as evidenced by the large fibre area (Figure 12b and c).

Effects of TiB 2 on microstructure and precipitation behaviour
Section 3.3 has shown that with an increase in the fraction of the γ ′ phase, the spherical γ ′ phase became cubic shaped and the M 23 C 6 phases precipitated from the γ matrix after TiB 2 addition, suggesting that the addition of TiB 2 affected the ageing behaviour of SD01-C (Fang et al. 2022;Tan et al. 2022a).
The variation in γ ′ phase fraction can be explained as follows. First, the TiB 2 particles provided more nucleation sites for the γ ′ phase, promoting the formation of precipitate nuclei via heterogeneous nucleation . Second, the mismatch in physical property between TiB 2 and the γ matrix increased the dislocation density (as demonstrated by EBSD in Figure 8g), which could reduce the growth activation energy energy (Tan et al. 2022a), providing more channels for the diffusion of solute atoms, accelerating the diffusion rate, and thus increasing the nucleation rate (He et al. 2021;M a et al. 2020). Therefore, the precipitation behaviour is enhanced, and the aging strengthening process is accelerated, forming a large number of γ ′ phase precipitates. Note that the shape of γ ′ precipitates was related to the γ-γ ′ mismatch. It was known that the γ ′ precipitates occurred as spheres at 0-0.2% lattice mismatch, became cubes at mismatches around 0.5-1%, and then became plates at mismatches above about 1.25% (Sims, Stoloff, and Hagel 1987). In this study, the lattice mismatch of γ-γ ′ in SD01 was calculated to be 0.3% using the JMat Pro Software, suggesting that the formed γ ′ precipitates were more in spherical shape. Previous studies have revealed that coherent strain energy has a significant effect on the evolution of γ ′ phase shape (Li and Chen 1998;Zhao et al. 2013). The γ ′ phases are mainly spherical because the anisotropic coherent strain energy could be negligible when the lattice misfit is small (Liu et al. 1998). When the γ ′ phases become coarse, the coherent strain energy increases and the γ ′ phases are transformed into cubic and irregular ). It may be concluded that the addition of 1 wt.% TiB2 increased the lattice misfit and thus reduced the coherent strain energy, promoting the change in morphology of the γ ′ phases.
Previous studies have demonstrated the classical reaction in Ni-based superalloy: MC + γ → M 23 C 6 + γ ′ (Fang et al. 2022;Yang et al. 2006). The thermal stability of primary MC carbide decreases significantly with a decrease in thermal exposure temperature and Al also promotes the formation of γ ′ (Sundararaman, Mukhopadhyay, and Banerjee 1988). In our study, MC phases distributed on sub-grain boundaries in the as-fabricated specimens were found to be rich in Ti, Nb, Mo and Ta (Figure 6c and f). After HT, the MC in SD01 and SD01-C was diffused to the matrix, while the γ ′ phase was precipitated from the matrix. Notably, M 23 C 6 was observed only in the SD01-C, not in SD01. The reaction of MC Figure 10. Engineering stress-strain curves of the as-fabricated and heat-treated original and SD01-C: (a) at room temperature, (b) at 900°C, and (c) at 1,000°C; (d) a summary of the ultimate tensile strength (UTS) versus elongation at room temperature and at 900°C between the designed materials in this study and the literature Chen et al. 2022;Marchese et al. 2018;Sun et al. 2021;Tang et al. 2020;Wang et al. 2012;Yang et al. 2021;Zhang et al. 2022a;Zhang et al. 2022b;Zhou et al. 2020). carbides with the matrix to form M 23 C 6 carbide is an element diffusion-controlled process in which Nb diffuses to the matrix, and Cr diffuses to the carbide . During HT, the Ti, Nb and Ta elements diffuse to the γ ′ phase to replace the Al elements so that the formation of Ni 3 (Al, Ti, Nb, Ta) is easier compared to that of Ni 3 Al because of the lower required formation energy (Park et al. 2022). Furthermore, the addition of TiB 2 promoted the precipitation of MC and M 23 C 6 , as well as lowered the transformation temperature, confirming that the M 23 C 6 phase could be formed only in SD01.
In addition, the EBSD (Figure 8g and h) analyses demonstrate that the grain became coarse after HT, while TiB 2 addition refine the grain size before and after HT. Figure 13 shows the effects of the TiB 2 particles on promoting grain nucleation during the LPBF process. A large number of sub-grains were formed during the ageing HT, while M 23 C 6 type carbides and the γ ′ phase precipitated at the sub-grain boundaries to inhibit sub-grain growth, resulting in a decrease in grain size after HT.

Possible strengthening mechanisms
The tensile test demonstrates that the yield strength of SD01-C was improved compared with that of the original SD01 at RT and at elevated temperatures. The improvement in mechanical performance might be attributed to various strengthening mechanisms, which  primarily include the following: (1) grain boundary strengthening, induced by the grain refinement, which follows the Hall-Petch relationship (s HP ); (2) secondphase strengthening induced by TiB 2 addition and γ ′ phase precipitation (s Sp ); (3) solid-solution strengthening (s SS ), determined by the modulus mismatch and lattice mismatch between solute atoms and solvent atoms; (4) dislocation strengthening (s D ) induced by increased dislocation density; and (5) load-bearing strengthening (s Load ) caused by the stress redistribution between the reinforced particles and the matrix.
The solid solution hardening of the Ni-based superalloy matrix is determined by the effect and concentration of each element as follows (Xu et al. 2020): in which c i is the degree of solubility of atomic species and is substituted using the data from the EDS of the γ-Ni matrix, and k i is the strengthening index of each element (Roth, Davis, and Thomson 1997). The s SS of the SD01-AB, SD01-HT, SD01-C-AB, and SD01-C-HT was calculated as 286.08, 297.68, 262.23 and 296.04 MPa, respectively. The contribution of the γ' phase through HT and ageing may be expressed as follows (McLean 1985;X u et al. 2020): where M is the Taylor factor, G is the shear modulus, b is the Burgers vector, and L s is the spacing between the precipitates, which is determined by f g ′ , the volume fraction of γ', and d g ′ , the size of γ', using the following equation (Goodfellow 2018): where the L s of the SD01 and TiB 2 modified SD01 was calculated as 167.74 and 135.83 nm, respectively. Therefore, the contribution of γ' to strength was calculated as 385 and 476 MPa. In addition, s Oro from the TiB 2 particles formed by the matrix is expected, consistent with the Ashby-Orowan relationship (Shang et al. 2019): where G is the shear modulus of the Ni-based alloy matrix, b is the Burgers vectors, f is the volume fraction of the TiB 2 particle and X is the average diameter of the TiB 2 particle. In this study, f is 1% and X is 600 nm. Hence, the increase in the yield strength of SD01 as a result of the TiB 2 particles was calculated as 132 MPa. Finally, load-bearing strengthening can be estimated as follows (Chen et al. 2015): where s m is the yield strength of the SD01 matrix (721 MPa), and V p is the volume fraction of the reinforcing particles, so s LB is 10.8 MPa. Figure 14 summarised the calculated strengthening contributions from different mechanisms compared to the experimental results; the calculated yield strength values of the SD01-AB, SD01-HT, SD01-C-AB and SD01-C-HT were 728.42, 1087.11, 852.26 and 1313.52 MPa, respectively. The calculated results of AB specimens were close to the actual experimental results. The calculated yield strength of SD01-HT was slightly lower than the experimental value, while the calculated value of SD01-C-HT was slightly higher than the experimental value, which might be attributed to the regional locality of the precipitates, the size of the precipitates examined in the calculation and the formed metallurgical defects, which can also affect the calculated values Lee et al. 2022). Based on the theoretical calculation of yield strength in Figure 14, the deviation induced by TiB 2 addition in the AB specimens may be attributed to Orowan strengthening and load-bearing strengthening. In addition, γ' phase precipitation played an important role in improving the yield strength of the heated specimens. Note that the contribution of dislocation strengthening in SD01-C-HT was obviously higher than that in SD01 after HT, indicating that TiB 2 addition was more effective in promoting the formation of recrystallisation than the role of grain growth in the HT process.
The elevated-temperature tensile tests presented in section 3.4 confirmed that TiB 2 addition significantly improved the material's elevated temperature strength and elongation. The yield strengths of SD01 before and after HT were similar under 900°C and 1,000°C, indicating that the spherical γ' phase gradually dissolved with an increase in temperature. Equation 14 shows that the addition of 1 wt.% TiB 2 contributed to strengthening the 142.8 MPa stresses. Notably, M 23 C 6 -type carbides induced by HT were relatively less unstable at high temperatures, which cannot provide sufficient reinforcing effects . However, the hightemperature tensile testing revealed that MC-type carbides were excellent reinforcing phases at high temperatures. The deviation between SD01 and SD01-C can thus be expressed as follows: where the solution strengthening deviations of the AB and HT are −23.85 MPa and −1.64 MPa, respectively, and the yield strength can be found in Figure 10b. Therefore, the contribution of carbides to strength of SD01 and SD01-C was calculated to be 44.24 and 124.21 MPa, respectively, confirming that carbides play an important role in improving the elevated strength of SD01-C material.

Conclusion
In this study, a novel crack-free precipitation strengthened Ni-based superalloy was designed to improve both LPBF processability and mechanical performance. The effects of 1 wt.% TiB 2 particle addition on strength were also systematically investigated in an SD01 composite (SD01-C). The following conclusions were drawn from this study: 1. The elements Al, Ti, Nb and Ta were optimised to prevent crack formation in designing the precipitation-strengthened Ni-based superalloy using RSM. The contents of the Al, Ti, Nb and Ta elements for the designed crack-free SD01 alloy were 1.94%, 2.4%, 1.5% and 1.25%, respectively. 2. The added 1 wt.% TiB 2 played a significant role in microstructure evolution, in which the grain morphology was altered from columnar to cellular structures in the SD01-C material. Furthermore, a large number of in-situ precipitates (e.g. γ ′ and M 23 C 6 ) were formed in the heated SD01-C because of the heterogeneous nucleation. The morphology of the γ ′ phase was altered from spherical to cubic structures, primarily induced by the TiB 2 addition, which decreased the Gibbs energy change from γ to γ ′ . 3. The elevated temperature strength of SD01-C increased with the addition of TiB 2 particles. Compared to SD01-AB, the added 1 wt.% TiB 2 contributed to over 90% improvement in the UTS values from 266.35 MPa to 509.51 MPa under the 900°C condition. After HT, the UTS values of SD01 and SD01-C were found to be 252.03 and 437.43 MPa, respectively, as a result of recrystallisation and grain growth. These findings indicate that TiB 2 played an important role in enhancing high-temperature properties.

Data availability
Data will be made available on request.

Disclosure statement
No potential conflict of interest was reported by the author(s).