Correlations of cracking with scan strategy and build geometry in electron beam powder bed additive manufacturing

Additive Manufacturing 32 (2020) 101031

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Full Length Article

Correlations of cracking with scan strategy and build geometry in electron beam powder bed additive manufacturing

T

Y.S. Leea,b,*, M.M. Kirkab,c, J. Fergusonb, V.C. Paquitb,d a

Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA Manufacturing Demonstration Facility, Oak Ridge National Laboratory, Knoxville, TN, USA c Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA d Electrical and Electronics Systems Research Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA b

A R T I C LE I N FO

A B S T R A C T

Keywords: Cracking Scan strategy Build geometry Ni-based superalloy Additive manufacturing Near-infrared camera Simulation

The extension of metal additive manufacturing (AM) to non-weldable Ni-based superalloys remains a challenge for the electron beam melting process. Various cracking mechanisms, including solidification, liquation, strainage, and ductility dip cracking, make it difficult to fabricate traditionally non-weldable Ni-based superalloys using the AM process. Because airfoil geometries are highly complicated, the correspondingly complex thermal signatures lead to various types of cracking in geometries that are under severe mechanical restraints during the printing process. This work aims to understand the correlations between cracking, scan strategy, and part geometry in airfoil geometries. Crack locations were monitored via an in-situ near-infrared camera during printing. A part-scale finite element method (FEM) was used to reveal cracking mechanisms. New scan strategies that avoided cracking were utilized in an FEM simulation. The present work demonstrates the potential for scan strategy optimization to manipulate stress distribution and the resultant microstructure of parts for industrial applications.

1. Introduction Additive manufacturing (AM) is considered a game-changer in the manufacturing industry, which has traditionally used subtractive manufacturing methods. AM offers a greater flexibility in part geometry by enabling engineers to create near-net shapes without material waste [1]. Thanks to this ability, AM technology has gained popularity, particularly in the turbine and aerospace industries, which want to improve energy efficiency. In the last couple of decades [2], the development of stronger high-temperature materials and the optimization of cooling methods has allowed for an increase in service temperature. AM has aided in these developments by enabling the tailoring of microstructure and the production of innovative cooling channel designs. However, the extension of metal AM to Ni-based superalloys (particularly to non-printable Mar-M247 and IN738 alloys [3]) is still challenging because of a lack of understanding about the correlation between the process and the resulting material properties. Electron beam melting (EBM) can alter process parameters and scan patterns by utilizing high beam deflection speeds and controlling the on and off time of the beam. These unique features enable operators to change spatial and temporal energy density within a given layer.

⁎

Consequently, the microstructure and mechanical properties of a specific layer become controllable. Helmer et al. [4,5] showed how to produce either columnar or equiaxed grain structures of IN718 by controlling process parameters (e.g., line offset, beam speed, and rotation). The capability of site-specific microstructure control was demonstrated by Dehoff et al. [6], who altered local process parameters and scan patterns (i.e., raster and spot-melting) to create the letters “DO-E.” The letters consisted of equiaxed grains, while the background columnar structures. Raplee et al. [7] extended the capability to a more complex bracket design in which cross sections continuously changed along the build direction. Raster and spot-melting scan strategies were used to produce columnar and equiaxed structure. Raplee et al. also showed that thermographic data (i.e., infrared camera data) can be used to identify microstructure variations in a part. Lee et al. [8] reported that it is possible to induce the desired thermal gradient (G) and solidification rate (R) by employing the raster, spot-melting, and ghost beam scan strategies in EBM. Kirka et al. [9] reported that the mechanical properties of cubic parts that were fabricated using raster and spot melting scan strategies were either anisotropic for columnar structures or isotropic for equiaxed structures. E. Chauvet et al. [10] reported that crack-free single crystals are achievable in Ni-based

Corresponding author at: Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA. E-mail address: [email protected] (Y.S. Lee).

https://doi.org/10.1016/j.addma.2019.101031 Received 22 August 2019; Received in revised form 4 December 2019; Accepted 31 December 2019 Available online 11 January 2020 2214-8604/ © 2019 Published by Elsevier B.V.

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that the energy density should be lowered by 10 %, corresponding to a 36 % reduction of the build area. The results indicated that beam return time should be considered when producing the same microstructure at a different build scale/geometry. Lee et al.'s following research on EBM showed that the dynamic evolution of thermal stresses and cracking tendencies can vary with the scan pattern and build geometry in Nibased superalloys. The work also showed that cracks were found only at specific locations due to conditions that produced susceptibility to solidification cracking. Cracking may be minimized by manipulating the scan pattern for the corresponding geometry. Leicht et al. [14] showed how part geometry (i.e., thickness and build angles) influences microstructure in the selective laser-melting (SLM) process. The authors reported that a part with a tilting angle below 45° produced primarily large elongated grains parallel to the build direction, while a vertical part produced a predominantly random texture. Also, they showed that a build thickness of 0.4 mm was critical for avoiding large elongated grains in the part. Cracking can be mitigated by adjusting process parameters if there is an understanding of the timing and location of the cracking. In EBM, it is known that the evolution of cracking and porosity defects can be observed with in-situ near-infrared (NIR) imaging [12,15]. In this study, the location of cracking was monitored with in-situ NIR imaging at various heights of a complex airfoil geometry. A continuum FEM was used to understand the complex interactions among scan strategy, part geometry, and cracking susceptibility. Lastly, new scan strategies were tested using an FEM model to mitigate/eliminate cracks from the complex part and to reduce deformation during the EBM process. The findings from this study can be further used to establish the design rules for a crack-free part with complex geometries.

Table 1 Nominal composition of Inconel 738LC powder meeting AMS5410™ compositional limits. Element

Cr

Ni

Ti

Al

Ta

W

Nb

Mo

Weight %

16.0

Bal.

3.45

3.45

1.75

2.6

0.85

1.75

superalloys by tight control of EBM process parameters. However, they noted that maintaining favorable melting conditions is challenging in complex geometries because it requires an understanding of the changes in process parameters and scan strategies that can maintain favorable conditions. Various cracking mechanisms, including solidification, liquation, strain-age, and ducility dip cracking, make it difficult to use the EBM process to build non-weldable Ni-based superalloys [3,11]. Although the cracking mechanisms are analogous to those in welding, the EBM process has to contend with complex thermal signatures due to the broadly varying and complex geometries that it is used to produce. That leads to complex interactions between process parameters, scan pattern, part geometry, which temporally and spatially vary the susceptibility to cracking [10,12]. Subsequently, AM of complex parts requires a massive and iterative optimization process that retards the wide adoption of EBM processes in industry. Therefore, a fundamental understanding of the correlation between scan strategy, microstructure, cracking, and part geometry is required to build an actual airfoil component. It is well known that the use of thermal cycle variation to alter microstructure is dependent on process parameters. However, few studies account for the interaction of part scale/geometry with process parameters, scan pattern, and the resultant part properties in regard to cracking. Babu et al. [12] have reported that thermal signatures at different locations are sensitive to scan strategy and/or part geometry. Using a high-speed camera, the intensity and motion of an electron beam building a complex geometry were recorded. The optical intensity showed that thermal signatures can be different at different locations due to the (1) approach pattern to the location, (2) dwelling time at the location, and (3) departure pattern. Lee et al. [13] have investigated the role of part scale/geometry in an EBM process using the spot-melting scan strategy. In this work, the values of G and R were calculated from 16 × 16 mm and 20 × 20 mm cross sections of a simple cube geometry using a low-fidelity finite element method (FEM). The results suggested

2. Experimental and modeling setup 2.1. Electron beam melting An Arcam Q10 machine was used to create turbine blades on a 304 stainless steel start plate with dimensions of 150 × 150 × 10 mm. The EBM system operates in a controlled vacuum chamber environment with 2 × 10−3 mBar of Helium gas. A preheat temperature of 1000 °C was used for the build. An NIR camera built-in to the machine was utilized to capture images of each layer immediately after melting was completed. Inconel 738 feedstock powder produced by gas atomization

Fig. 1. Airfoil geometry with an angle of 45° and the sectioned area for numerical simulation. 2

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Table 2 Material properties of IN738 used in stress analysis. Temp(ºC)

Density (Kg/m3)

Thermal Conductivity (W/m-ºC)

Specific Heat (J/Kg-ºC)

Thermal Expansion (ºC−1)

Young’s Modulus (GPa)

Poisson Ratio

Yield (MPa)

100 500 600 800 1000 1050 1100 1225 1337

– – – – 7760 – – – 7510

11.7 – – – 24.7 – 27.7 – –

442 – – – 819 915 – – –

11.9E-06 13.9E-06 – – 17.4E-06 18.3E-06 – – –

213 187 – – 145 138 – 108 1.00

0.33 0.33 – – 0.33 0.33 – 0.33 0.48

– – 750 600 200 – 90 – –

Fig. 2. Sensitivity analysis of time step vs. maximum stress value. The value converges to 155 MPa as it approaches a smaller time step. Note that the stress distributions are almost identical at dt = 1.29e-2 s and dt = 6.45e-3 s.

Fig. 3. Raster scan pattern: the blue and red colors represent the regions where the beam starts and ends, respectively. The electron beam sequentially melts from (a) to (d) (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).

Fig. 4. CAD geometry for the airfoil fabrication showing a drastic change of geometry within a 10 mm change in height of the airfoil.

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Fig. 5. Observed cracking tendency on interaction with geometry and scan direction.

Fig. 6. Observed cracking in actual airfoil through in-situ NIR monitoring. The crack is consistent in the platform region (a)-(c) regardless of geometry and scan direction, whereas the crack is found at the tail edge (d)-(e) of the blade. The crack stays for 100 layers (layer thickness =50 μm) and disappears (f) as the height increases.

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sectioned parallel to the build direction. Standard metallographic techniques were used to prepare samples for an optical microscope. Part dimensional accuracy was investigated using a 7-axis Faro Quantum Arm laser scanner. The 3D-scanned data from the as-printed airfoil was compared to the CAD geometry using GeoMagic (3D systems corp.), which reveals undersized or oversized locations in a part. 2.2. Modeling approach and boundary conditions To understand the correlations between temperature distribution and cracking susceptibility, it is important to examine the spatial and temporal evolution of stress during the melting process across all locations in a given layer. A physics-based FEM simulation was implemented through the Abaqus AM plug-in module [16]. The AM part geometry in STL (stereolithography) format was first discretized with finite elements. Then, the scan parameters from the EBM machine (e.g., power, beam locations, beam size, speed, and travel distance) were incorporated into the input file through an intersection module. The module finds intersections between the finite element meshes and the scan path. During the analysis, each intersection can either be an undeformed or deformed shape of the part. A progressive element

Fig. 7. Crack observation through optical micrograph. The image shows good correlation between the in-situ NIR image in Fig. 6(d)–(e) and the optical image. [21].

was used as the powder in the EBM process. The nominal chemistry is listed in Table 1, which is consistent with the Inconel 738 composition in AMS5410™. The layer thickness was 50 μm. The airfoil samples were

Fig. 8. Stress (S22 along the y-axis) development during melting time at (a) 6.2 s, (b) 7.7 s, (c) 8.4 s, and (d) end of melting. 5

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Fig. 9. Stress at the trailing edge starts to develop as the beam starts to split the heating due to the curved shape of the blade. (a)-(c) show the stress distribution at 2.4 s, 3.0 s and 5.0 s. (d)–(f) represents corresponding temperature distribution at 2.4 s, 3.0 s, and 5.0 s.

angle of 45 degrees. The height of the airfoil was 130 mm. The geometry of the airfoil and the cross section are shown in Fig. 1. The mesh geometry had 47,790 hexahedron elements. The DC3D8 and C3D8 types of elements were used to obtain thermal and stress distribution during the printing process. Since the bottom region of the airfoil was fused to the substrate, it is assumed that the bottom surface was fully constrained in all x, y, and z directions during the simulation. The material properties used in the simulation are given in Table 2. Fig. 2 shows that the variation in the size of the time step changed the predicted maximum principal stress value. When the time step was reduced, the stress values increased and converged to 155.0 MPa. The computation time also inversely correlated with time step size. The simulation time increased from 15 min. at dt = 1.29e−1s to 330 min at dt = 6.45e-3s. Notice that the stress distribution is almost identical at dt = 1.29e-2s and dt = 6.45e-3s, although the simulation time is doubled at dt = 6.45e-3s. Therefore, in the present study, the time step of 1.29e2 s was selected to satisfy both accuracy and efficiency.

activation method was applied to account for the addition of material at any given point during the printing. The powder bed was inactive at the beginning of the simulation and was activated according to the scan path. An arbitrary number of heating events (i.e., electron beam power) was incorporated into the active elements in both time and space (=scan path). The convection and radiation cooling were computed on a continuously activated part surface that accounted for the current shape of the part during printing. Thermomechanical models were sequentially coupled, and it was assumed that the mechanical stress did not influence phase transformation and temperature evolution. The transient heat transfer and quasi-static stress balance equation were calculated based on the Abaqus finite element solver. More details on the AM module and the balance equations can be found in earlier literature and in the software user manual [16–18]. The electron beam heat source is considered as a point-concentrated heat source due to the relatively large element size compared with the melt pool. In this work, the moving heat source is described in a given mathematical equation as follows:

Q˙ (x , y, z , t ) =

2Pη y2 z2 (x + vx t )2 exp ⎛− + + ⎞, abcπ π a b c⎠ ⎝ ⎜

2.3. Scan strategies

⎟

(1)

The raster scan is the most common scanning pattern in EBM because of its easy implementation and simple space-filling algorithm [5,19,20]. The raster scan moves linearly from one point to another point with varying speed, current, and melting distance. Then, it jumps to the next line by a set hatch spacing. Fig. 3 illustrates the scan pattern used for the airfoil at a height of 44.75 mm. The beam linearly moves from the (a) top left to the (d) bottom right region. Fig. 4 shows changes in the cross-sectional geometry corresponding to a 10 mm change in the height of the airfoil. The computer aided design geometry showed that a drastic change occurred with a small change in height. As discussed in the introduction, optimization of scan strategies as a function of cross-sectional geometries is vital to mitigating cracking. Typically in EBM, a raster scan melts the powder using a predefined

where Q is heat flux, P is the nominal power, η is the absorptance, vx is travel speed of the moving heat source, and a, b, and c are the dimensions of the heat source along the x, y, and z axes, respectively. The heat loss through the surrounding environment is considered to be by radiation since the EBM process operates in near vacuum conditions such that convectional heat loss can be assumed to be negligible. The thermal radiation is expressed as

qrad = εσ ((T − Tz ) 4 − (Tp − Tz ) 4),

(2)

where ε is the material emissivity, σ is Stefan-Boltzmann constant, Tz is absolute temperature, and Tp is preheat temperature. A cross section of the airfoil was taken at 44.75 mm with a tilting 6

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Fig. 10. Temperature-stress-time plot at cracked and non-cracked regions. The intersection of tensile stress with cracking susceptible temperature range (= 1145 °C–1305 °C) is found at the trailing edge region. The cracking occurs in temperature range (1225 °C–1250 °C) in the crack susceptible region.

Fig. 11. Melt pool evolution at (a) 7.3 s, (b) 8.0 s, and (c) 8.6 s at the leading edge region. The volume of the melt pool varies with time because of the characteristic scanning feature in the EBM machine.

from the group of unmelted points. More details are discussed in Section 3.2.

velocity and melting sequence, while spot-melting applies individual spots at desired locations with a predefined beam-on time and moving sequence [8]. In this study, two new scan patterns, called random spotmelting and random raster scan, are proposed and tested for the minimization of the impact of radical geometrical transformation. Random spot-melting and random raster scan each randomly select their starting position. Then, melting occurs at a random point selected

2.4. Observation of cracking via near infrared camera Babu et al. [12] showed that in-situ NIR can be used to diagnose the tendency to crack during printing. Fig. 5 shows the location of cracks 7

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Fig. 12. Plot of (a) thermal gradient G, (b) solidificaton rate R, and (c) cooling rate. An abrupt transition is observed at the leading edge region in the solidification rate and the resulant cooling rate [21].

Fig. 13. Stress distribution along the y-axis with (a) random spot-melting and (b) raster scan pattern. Random spot-melting removes the stress concentration from the trailing edge region of the airfoil.

optical micrograph image to verify the locations of cracks. The crack detected by NIR at the trailing edge region of Fig. 6(d)–(e) is found at an identical location in the optical micrograph shown in Fig. 7. This confirms that in-situ observation of cracking via NIR imaging is a reasonable method for identifying the where cracks form during the EBM process. Note that cracking was observed at the leading edge region in the optical micrograph but was not detected in the NIR image. The NIR camera captures the image at the end of the melting stage. Thus, it is assumed that the crack at the leading edge region occurred during cooling, rather than during melting.

identified with the in-situ NIR image from the Q10 machine. Fig. 5 shows that cracking periodically appears and disappears as the beam changes direction and location. The wide rectangle on the left side of each image is the building part with a tilting angle of 45°. The thin rectangles on the right side of each image are the supports. The black arrow indicates the scan direction at a given layer. Note that cracks are observed only when the scan direction is not parallel to the long edge of the part. The in-situ NIR technique was also applied to the complex airfoil geometry. As shown in Fig. 6(a)–(c), the location of cracking is consistent, regardless of geometry or scan direction. Interestingly, the cracking location moved to the trailing edge region in Fig. 6(d)–(e). Eventually, the cracks disappear as the build height increases, as in Fig. 6(f). This indicates that the cracking location interacts with part geometry and scan strategy. Fig. 7 shows that an in-situ NIR image can be compared with an

3. Results and discussion 3.1. Crack prediction Three-dimensional thermomechanical simulations were performed 8

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Fig. 14. Random raster scan pattern. (a) Stress accumulation and (b) stress relaxation. This scan pattern reheats the same areas multiple times and relaxes the high stress developed.

susceptible temperature range (= 1145 °C–1305 °C) intersects with S22 tensile stress at the trailing edge region in Fig.10(b), while there is no intersection found in Fig. 10(c). The results show that the crack initiates at about 6–9 s, in the temperature range of approximately 1225–1250 °C, and then propagates to the end of melting. Therefore, solidification is a probable cracking mechanism at the trailing edge region. Fig. 11 shows melt pool evolution over time at the leading edge region. As melting continues, the melting pool volume decreases because of the characteristic melting feature of the Q10 machine (e.g., it changes scan parameters to maintain the input energy constant). Different melt pool geometries and shapes lead to a change in solidification conditions and consequently impact solidification morphology. Thermal gradient G, solidification rate R, and cooling rate can be predicted by using a low-fidelity model [27], as shown in Fig. 12. The thermal gradients shown in Fig. 12(a) are roughly uniform across the blade. However, note that an abrupt transition in solidification rate is observed at the leading edge region in Fig. 12(b) and that this transition region corresponds to the region where melt pool volume changes in Fig. 11. This implies that microstructural changes can occur at this transition region due to variations in the solidification conditions. Although microstructural change requires experimental confirmation, this appears to be a culprit of cracking.

to reveal the cracking mechanism in the blade geometry. Fig. 8 shows the stress development over time. Stresses along the y-axis (S22) at the trailing edge region in Fig. 8(a) continually increase through the end of the melting stage in Fig. 8(d). This high stress region is consistent with the cracking region found in the experimental specimen shown in Fig. 7. Fig. 9 shows the initiation of tensile stress at the trailing edge of the airfoil where the cracking was observed. At the beginning of melting, tensile stress develops close to both the leading and trailing edges, as shown in Fig. 9(a). The tensile stress at the leading edge region gradually diminishes as the beam moves and raises the temperature of the region, represented in Fig. 9(c) and (f). However, the tensile stress at the trailing edge region continuously increases. The tensile stress at the trailing edge appears as the beam starts to be split into two beam sources due to the curved geometry, as shown in Fig. 9(d) and (e). The region in between the split beam undergoes relatively rapid cooling because, unlike the regions around it, it is not being actively heated by the beam. This geometry-induced inhomogeneous cooling leads to nonuniform stress development at the trailing edge. This stress continues to increase until the end of melting, shown in Fig. 8(d). The variations in temperature and stress over time are plotted in Fig. 10, which shows that cracking during melting occurs when a susceptible temperature and high stress region coexist [22–24]. The initiation and propagation of hot cracking occurs when the liquid film exists until the end of dendrite coalescence. It is generally believed that a larger solidification temperature range (ΔTL-S = Tliquidus - Tsolidus) increases the chance of hot cracking at the grain boundaries [25] because the liquid film is present at a lower temperature. When normal tensile stresses are produced by thermal gradients during printing, the dendrite grain boundaries cannot accommodate the stresses and cracks are formed. The amount of liquid film can be determined through the volume of solid fraction. The range of solid fraction is estimated as a function of temperature by the Scheil–Gulliver method, using ThermoCalc [26] software. Because the Scheil equation does not examine coalescence of dendrites, the crack-susceptible temperature range should be empirically defined. Prior literature [24] states that when the solid fraction is between 0.7 and 0.98, dendrite arms have nearly coalesced such that the liquid cannot flow into the inter-dendritic region to cure cracks. A material thus becomes susceptible to hot cracking. The temperatures corresponding to these solid fractions are 1145 °C and 1305 °C, respectively. Note that, in Fig. 10, this cracking-

3.2. Crack mitigation New scan strategies were engineered to mitigate non-uniform stress concentration and the resultant cracking in the blade geometry. A novel random point scan pattern was applied to the airfoil. The scan pattern divides the geometry into a group of discrete points on a uniform triangular grid of a given point spacing. The first melting spot occurs at a random point on the grid, and then the next melting spot is chosen at random from the remaining group of unmelted points. This process repeats until all points in the blade geometry have melted. The stress distributions generated by the random point-net and by the raster scan are compared in Fig. 13. The random point-net simulation used process parameters of 190 W beam power, 0.25 ms beam on-time, and 200 μm spacing. The numerical prediction in Fig. 13(a) shows that significant stress relaxation is achieved by using the new random point-net scan strategy. The stresses that were observed at the trailing edge region of the raster scan in Fig. 13(b) were mitigated by the random point-net in Fig. 13(a). It seems that the point-net scan led to a more uniform stress 9

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Fig. 15. Distortion in airfoil part using (a) raster and (b) spot-melting scan strategy. This shows that part deformation can be mitigated by controlling of the scan pattern.

3D airfoil geometry with 3586 layers to demonstrate model feasibility and to show the influence of scan strategy on part distortion. A comparison of the two scan strategy models is shown in Fig. 15. The models use a layer lumping methodology, which allows the use of a relatively coarse mesh for faster simulation [28]. In this demonstration, a power of 840 W was used for both the spot-melting and the raster scan models. A beam on time of 0.25 ms and an inter-spot spacing of 200 μm were set for spot-melting. A speed function of 55, which is one of the optimization functions [8,29,30], was applied to the raster scan to maintain a constant input energy. Fig. 15 illustrates the part distortion in an actual airfoil with a height of 179.3 mm. Generally, higher distortion was found at the front corners of the platform and at the lower side of the shroud. For the spot-melting case in Fig. 15(b), high distortion was also observed at the trailing edge of the blade. Moreover, spot-melting produced a wider range of high distortion at the bottom of the platform and in the shroud. If cracking is considered, it seems the raster scan is the better option for minimizing the distortion of the airfoil part. However, although no optimization schemes were applied to the spotmelting strategy, the spot-melting produced a smaller maximum distortion (i.e., 3.5 mm in raster vs. 2.5 mm in spot-melting). The development of an optimization scheme is required for the spot-melting scan

distribution in the blade geometry, which possibly prevented stress from concentrating in the cracking-susceptible region. Another new scan strategy, named random raster scan, was used to control stress development and is shown in Fig. 14. This scan pattern is a mix of raster and random spot-melting scan patterns. The pattern randomly picks two points as the start and end points of a raster scan pattern. Every point along this line is considered to be melted. Then, a new end point is randomly selected from the group of unmelted points. This strategy used a power of 190 W and a constant beam velocity of 1214 mm/s. Fig. 14 shows that the random raster scan forms relatively high stress at the beginning of the melting and then relaxes the stress as it repeats the scanning. This scan pattern produces results similar to post-heat treatment in other processes (e.g., welding) because it reheats the same areas multiple times and relaxes the high stress developed in those areas. The advantage of the random raster scan is that it can cut the melting time almost in half compared with normal raster scan strategies. 3.3. Influence of scan strategy on distortion The raster and spot-melting scan strategies were extended to the full 10

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Fig. 16. Comparison of a predicted distortion with a measured value for the raster scan.

the cracks from the blade and to reduce deformation during the EBM process. Key findings from this study are:

strategy to be applied to a complex geometry. Fig. 16 compares the predicted deformation with data from 3D scanning of the as-printed airfoil. The geometric deviation between the desired shape and the as-printed airfoil is shown in Fig. 16(a). For the inset, the blue color indicates undersized geometry due to asymmetric shrinkage and thermal distortion, whereas the red represents oversized geometry due to asymmetric expansion and thermal distortion. In Fig. 16, the predicted (b) undeformed (before printing, which is identical to original CAD geometry) and (c) deformed (after printing) geometries were superimposed for comparison with the scanning data. The cross-sectioned geometries were taken from the simulation at the height of 18 mm from the bottom of the airfoil. Large deformations were found at the lower left and right corners, 66.0 mm and 110.0 mm from the origin, respectively. Note that a small standout is observed at the 32.0 mm spot in Fig. 16(a). This is an Arabic numeral and was intentionally printed to distinguish this part from the others. The protrusion was not found in the undeformed geometry at the height shown in Fig.16(b) but was observed in the as-printed one in Fig. 16(c). This indicates a noticeable shrinkage along the build direction, which is precisely captured by the simulation. Fig. 16(d) shows that the deformation trend at each corner of the airfoil was reasonably well predicted by the raw predicted values, but the accuracy of the prediction can be further enhanced by calibration of the raw values. Previous literature and the present work show that EBM scan strategies enable manipulation of microstructure and stress distribution in an actual application. A potential application is to fabricate a single crystal, which has been reported in the AM literature [10]. However, because single-crystal fabrication requires highly sophisticated control of process parameters and a scan strategy that can preserve favorable local solidification conditions during printing, complex geometries still present a challenging issue for such fabrication.

• NIR imaging is a promising way to capture the spatial variation of cracking as a function of scan strategy and cross-sectional geometry. • The mechanical response to size, geometry, and scan strategy should be carefully investigated and controlled to prevent crack formation. • Geometry-induced inhomogeneous cooling leads to non-uniform tensile stress distribution for a given blade geometry. • Investigation of the variation in temperature and stress over time indicates that solidification is a probable cracking mechanism. • The proposed scan strategies show that cracking or distortion can be mitigated (or eliminated) by manipulating the scan patterns.

Author contributions Conceptualization, Y.S. Lee, M.M. Kirka, J. Ferguson and V.C. Paquit; validation, Y.S. Lee, M.M. Kirka; Formal analysis, Y.S. Lee and J. Ferguson; Investigation, Y.S. Lee; resources, M.M. Kirka and V.C. Paquit; data curation, Y.S. Lee; writing-original draft preparation, Y.S. Lee and J. Ferguson; Visualization, Y.S. Lee; writing-review and editing, M.M. Kirka; supervision, M.M. Kirka and V.C. Paquit, project administration, Y.S. Lee; funding acquisition, M.M. Kirka Declaration of Competing Interest None. Acknowledgements This research was sponsored by the US Department of Energy, Office of Energy Efficiency and Renewable Energy, Advanced Manufacturing Office under contract DE-AC05-00OR22725 with UT-Battelle, LLC. The authors thank Benjamin Stump, Matthew Ireland, Dr. Ahmed Hassan, Dr. Srdjan Simunovic, and Abigail Barnes for helpful support in preparation of this manuscript.

4. Summary and conclusions A continuum part scale model was used to understand the correlation between cracking, scan strategy, and part geometry. Crack locations were identified with NIR images during the printing process. Cracking occurred at the trailing edge of the airfoil as the beam started to split into two instances of heating due to the curved blade geometry. Using FEM, new scan strategies were proposed to mitigate/eliminate

References [1] A. Bandyopadhyay, B. Heer, Additive manufacturing of multi-material structures,

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