Solidification-driven orientation gradients in additively manufactured stainless steel

Solidification-driven Orientation Gradients in Additively Manufactured Stainless Steel

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Solidification-driven Orientation Gradients in Additively Manufactured Stainless Steel Andrew T. Polonsky, William C. Lenthe, McLean P. Echlin, Veronica Livescu, George T. GrayIII, Tresa M. Pollock PII: DOI: Reference:

S1359-6454(19)30718-9 https://doi.org/10.1016/j.actamat.2019.10.047 AM 15616

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Acta Materialia

Received date: Revised date: Accepted date:

22 August 2019 25 October 2019 31 October 2019

Please cite this article as: Andrew T. Polonsky, William C. Lenthe, McLean P. Echlin, Veronica Livescu, George T. GrayIII, Tresa M. Pollock, Solidification-driven Orientation Gradients in Additively Manufactured Stainless Steel, Acta Materialia (2019), doi: https://doi.org/10.1016/j.actamat.2019.10.047

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Graphical Abstract Solidification-driven Orientation Gradients in Additively Manufactured Stainless Steel Andrew T. Polonsky,William C. Lenthe,McLean P. Echlin,Veronica Livescu,George T. Gray,Tresa M. Pollock

Highlights Solidification-driven Orientation Gradients in Additively Manufactured Stainless Steel Andrew T. Polonsky,William C. Lenthe,McLean P. Echlin,Veronica Livescu,George T. Gray,Tresa M. Pollock

• 304L stainless steel manufactured via LENS was characterized in its as-deposited state in 3D using TriBeam tomography • Misorientation is found to increase along the solidification direction, in excess of 10° from the initial growth orientation • Orientation gradients are linked to chemical segregation occurring during the solidification

Solidification-driven Orientation Gradients in Additively Manufactured Stainless Steel

Andrew T. Polonskya,∗ , William C. Lenthea , McLean P. Echlina , Veronica Livescub , George T. Gray IIIb and Tresa M. Pollocka a Materials b Los

Department, University of California Santa Barbara, Santa Barbara, CA 93106, USA Alamos National Laboratory, Los Alamos, NM 87545, USA

ARTICLE INFO

ABSTRACT

Keywords: additive manufacturing tomography solidification microstructure TriBeam

A sample of 304L stainless steel manufactured by Laser Engineered Net Shaping (LENS) was characterized in 3D using TriBeam tomography. The crystallographic, structural, and chemical properties of the as-deposited microstructure have been studied in detail. 3D characterization reveals complex grain morphologies and large orientation gradients, in excess of 10°, that are not easily interpreted from 2D cross-sections alone. Misorientations were calculated via a methodology that locates the initial location and orientation of grains that grow during the build process. For larger grains, misorientation increased along the direction of solidification. For grains with complex morphologies, K-means clustering in orientation space is demonstrated as a useful approach for determining the initial growth orientation. The gradients in misorientation directly tracked with gradients in chemistry predicted by a Scheil analysis. The accumulation of misorientation is linked to the solutal and thermal solidification path, offering potential design pathways for novel alloys more suited for additive manufacturing.

1. Introduction Recent advances in additive manufacturing (AM) have led to increased interest in the process for low volume manufacturing of end-use components. Developed at Sandia National Laboratory over two decades ago as a rapid prototyping and weld repair technique, the Laser Engineered Net Shaping (LENS) process is a directed energy deposition (DED) technique derived from laser cladding processes which utilizes nozzles to blow powder into melt pools created using a laser heat source [1]. Although lacking the same geometric specificity as powder bed processes like Selective Laser Melting (SLM) or Electron Beam Melting (EBM), LENS is attractive due to its high deposition rates and larger build volumes, up to an order of magnitude higher than powder bed processes, allowing for the fabrication of largescale, fully-dense parts [2, 3]. LENS offers dimensional accuracy on the order of a 0.5 mm or less, with average surface roughness on the order of 20-50 microns, and has the flexibility to be used for repair operations or to add components to pre-manufactured parts, which is not possible in powder bed processes [4, 5]. Unlike powder bed processes, powder streams can be mixed or changed during production, offering the opportunity for joining of dissimilar materials via cladding or even functionally graded materials that are impractical for powder bed processes [6–10]. The wide scope of processing parameters is integral to the flexibility of additive manufacturing (AM) techniques, but can also create highly variable material properties. Key to this processing flexibility is the scan strategy, which ∗ Corresponding

author [email protected] (A.T. Polonsky)

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describes the manner in which the heat source traverses the part. The path of the heat source during deposition can strongly influence grain morphology and crystallographic texture in AM parts. In many powder bed processes, differences in the default scan strategy between machine manufacturers can lead to identical designs with vastly different mechanical behavior [11–14]. DED techniques are generally more limited in the choice of novel scan strategies, but large changes in texture, grain morphology, and residual stress in DED parts have been observed even by changing from a uni-directional to bi-directional raster scan strategy [15–17]. Other important process variables include laser power, travel speed, powder feed rate, and the working distance between the powder head and the substrate, all of which control the morphology of the deposited bead [18, 19]. The process also creates parts with highly anisotropic mechanical response, with parts exhibiting large changes in strength and ductility depending on their orientation relative to the build direction [20–22]. One approach to understanding physical processes with many variables is the use of process maps, which can help show empirical relationships between multiple parameters. This technique has been previously applied to laser welding processes [23], and has also been used to understand additive manufacturing processes, both with actual machine settings [24, 25] and the use of dimensionless parameters, which can help compare a variety of additive processes to each other [26]. These maps naturally lend themselves to process models which aim to capture the thermal history of a part during manufacture [27, 28]. Thermal models can be used to predict residual stress and extended to predict observed solidification microstructures using calculated thermal gradients and solid-liquid interface velocities [29– 31]. Thermal gradients and interface velocities will vary throughout solidification, and the increase of solidification velocity coupled with a decrease in thermal gradient leads to rapid evolution from plane front to cellular to dendritic growth modes in the LENS process. Incorporation of additional modelling approaches, such as kinetic Monte Carlo and Cellular Automata, can predict microstructures that may accurately capture the morphology of experimental samples [32–34]. However, these models are limited in capturing the full physics of nucleation and growth during solidification [35]. Another key limitation in microstructure prediction is the absence of orientation gradients, which are routinely observed in Electron Backscatter Diffraction (EBSD) scans of additive structures and are important to cracking and tearing processes [5, 21, 32, 36, 37]. A force is required to rotate the crystal in order to create changes in orientation, but the mechanism creating orientation gradients in additive structures is not well understood. To improve process models, more comprehensive characterization of as-built microstructures is required to understand the underlying processes governing microstructure evolution as well as process-property linkages. In this work, the origins of complex grain morphologies and orientation gradients in as-deposited additive microstructures are investigated via the full 3D microstructural characterization of a melt pool boundary in a LENSprocessed sample of 304L stainless steel.

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2. Experimental Bulk 304L stainless steel was fabricated using pedigreed micro-melt powder with a particle size range of 44-106 µm (Carpenter Powder Products) and composition as shown in Table 1. A vertical plate, with nominal dimensions of 100 mm long × 12.5 mm wide × 50 mm tall was built using an Optomec LENS Mr-7 system with a continuous wave ytterbium fiber laser with wavelength of 1070 nm. The build used a laser power of 800 W, a travel speed of 1.02 m/min, a powder feed rate of 33.7 g/min with 20% powder efficiency, resulting in a deposition rate of 400 g/hr. The build was conducted under inert Argon atmosphere (<5 ppm O2 ) flowing at 30 L/min. The build layer thickness was 0.76 mm and on each build layer a single contour trace was followed by an angled rectilinear hatch strategy with a hatch spacing

of 1.02 mm, yielding a hatch overlap of nominally 40% to minimize lack of fusion defects. The bidirectional raster strategy on each layer was rotated by 90° to create cross-hatching between subsequent build layers. Table 1 Chemical composition of the 304L stainless steel powder. C (wt.%)

Cr (wt.%)

Fe (wt.%)

Mn (wt.%)

Ni (wt.%)

Si (wt.%)

P (wt.%)

N (wt.%)

O (wt.%)

0.015

18.4

bal.

1.5

9.8

0.53

0.012

0.05

0.019

The material characterized in this work was taken from the upper region of the plate in its as-deposited state as shown in Figure 1(a). Samples from the upper portion of the plate were removed via wire electrical discharge machining to create free-standing pedestals for 3D characterization. The approximate location of the 3D dataset is also shown in Figure 1(b). 3D characterization was performed with the TriBeam system, a serial sectioning tool which incorporates a femtosecond laser into a dual-beam Scanning Electron Microscope (SEM) with Focused Ion Beam (FIB) [38]. The femtosecond laser is used for in situ micromachining within the vacuum chamber, imparting minimal damage to the sample surface due to the ultrashort pulse lengths while allowing for high material removal rates, roughly four to five orders of magnitude faster than FIB milling alone, enabling characterization of volumes on the order of a cubic millimeter [39]. A sample of the LENS-manufactured plate was characterized via TriBeam tomography using a slice thickness of 3 µm. A laser power of 280 mW with a focused spot size of roughly 50 µm was used for material removal. The laser-ablated surface was cleaned using the FIB at a glancing angle of 8°. FIB milling at glancing angles has been shown to minimize surface roughness arising from Laser Induced Periodic Surface Structures (LIPSS), which increases surface quality for EBSD [40]. EBSD data was collected on each slice with an in-plane resolution of 3 µm, resulting in square voxels with a side length of 3 µm. Over the course of two days, roughly 200 GB was collected across 80 slices, resulting in a dataset volume of 816 × 834 × 240 µm. 3D reconstruction was performed in DREAM.3D [41] to create a coherent volume. Several reconstruction variables were selected via parametric studies conducted in the BisQue platform [42], and details on the reconstruction and parameter selection process can be found elsewhere [43]. Briefly,

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Figure 1: As-deposited sample of 304L removed from uppermost portion of the plate (a). Line artifacts from the scan strategy are visible on the undisturbed top layer of the sample. Large area composite backscatter electron micrograph of a cross-section of the as-deposited sample (b). The approximate location of the 3D volume characterized in this work is highlighted, and surrounds the upper portion of a remaining melt pool boundary.

EBSD data was masked using a minimum confidence index (CI) of 0.1, grains were segmented using a misorientation tolerance of 2°, and grains smaller than 64 voxels (equivalent diameter of 14.9 µm and roughly five times smaller than the average grain size as determined from 2D analysis) were considered too small to be resolved and were removed.

3. Results 3.1. Grain Morphology and Misorientation

The fully-reconstructed 3D volume is comprised of 899 grains and is shown in Figure 2. The build direction was

chosen as the reference direction for inverse pole figure (IPF) coloring. Grain morphology can be characterized using zeroth-, first-, and second-order moments to create a best-fit ellipsoid of each grain [44]. The primary aspect ratio (PAR) of the best-fit ellipsoid of the grain is given by Equation 1: 𝑃 𝐴𝑅 =

𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑙𝑎𝑟𝑔𝑒𝑠𝑡 𝑚𝑖𝑛𝑜𝑟 𝑎𝑥𝑖𝑠 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑚𝑎𝑗𝑜𝑟 𝑎𝑥𝑖𝑠

(1)

Although the PAR does not fully capture 3D grain morphology, especially for complex grain shapes, it is a simple metric for assessing grain morphology, with columnar grains having lower values of PAR, near zero, while equiaxed grains will have higher values of PAR, near unity. Despite the small misorientation tolerance of 2° used to segment grains in the volume, several grains were found to contain large internal orientation gradients, in excess of 10°. These misorientations are calculated using the average orientation of a grain as the reference. A grain’s average orientation

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Figure 2: Fully reconstructed volume of 304L stainless steel sample manufactured via LENS. EBSD data is shown in IPF coloring, with the build direction taken as the reference direction. This sample was characterized via TriBeam tomography in its as-deposited state.

is found by selecting a seed orientation for the grain, which can be done randomly or using some metric such as the orientation at the centroid of the grain. The symmetric equivalent closest to the seed orientation is then computed for each voxel in the grain using symmetry operators of the sample crystal to place all of the orientation in the fundamental zone, or the region in rotation space in with each physically distinct misorientation (or orientation in regards to a specific reference frame) is only represented once [45]. Orientations are then averaged using quaternion averaging, which is a good approximation to the rigorous technique involving quaternion exponentiation. The calculated PAR for each grain is shown as a function of the maximum misorientation from the grain average orientation in Figure 3(a), with marker areas that are directly proportional to the volume of the grains. Grain morphology does not appear to strongly influence the maximum misorientation within a grain, as grains with both low and high values of PAR contain highly misoriented regions. However, there does appear to be a strong positive correlation between grain size and maximum misorientation within a grain; only 19 (2.11%) of the grains contain maximum misorientation above 10°, yet they comprise 54.3% of the dataset volume. The largest grain, comprising 20.2% of the dataset volume, has a maximum misorientation from the grain average of 12.5°, and is shown in Figure 3(b). This grain has a complex morphology not readily captured by simple shape metrics, and the large orientation gradients can be seen as large changes in IPF color throughout the grain.

3.2. Process-Informed Characterization

In order to better understand the origin of these large gradients in orientation within grains, it is useful to in-

corporate details of the manufacturing process. Calculation of misorientation from the grain average orientation is straightforward, as DREAM.3D has already incorporated this capability [41], but the directional nature of solidificaAT Polonsky et al.: Revised article submission for Acta Materialia

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Figure 3: Primary aspect ratio as a function of the maximum misorientation within each grain (a). Marker areas are directly proportional to the volume of each grain. Misorientations were calculated from the average orientation of each grain. The largest grain in the characterized volume shown in IPF coloring, using the build direction as the reference direction (b).

tion in additive and welding processes means that the starting orientation of a grain when it nucleates in the liquid can be a more useful reference orientation to characterize the solidification process. There are several columnar grains in the volume which formed near the center of the melt pool and can be analyzed to determine a representative nucleation orientation. One such columnar grain is shown in Figure 4, which has a PAR of 0.165 and has a readily-identifiable nucleation point near the bottom of the 3D volume where the grain tapers down to a thin region. This region contains the earliest parts of the grain to solidify during the LENS process. The orientation measured at the centroid of the bottom-most slice of this grain was chosen as a new reference orientation to better capture the nucleation orientation

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Figure 4: A highly-columnar grain with large orientation gradients. EBSD data shown in IPF coloring with the build direction as the reference direction (a). Spatial distribution of misorientation using the nucleation orientation as determined from the bottom of the grain (b). Misorientation increases along the build direction, following the solidification direction of the columnar grain.

of the grain. When using the grain average orientation, the maximum measured misorientation was found to be 6.24°. However, when the nucleation orientation was chosen as the reference orientation, the maximum measured misorientation increased to 7.70°. The spatial distribution of the measured misorientation is shown in Figure 4(b). These misorientations are not randomly distributed throughout the grain, but can be seen to increase along the direction of solidification for this grain, with the highest calculated misorientations clustered around one small region of the grain near the top of the 3D volume. The columnar grains can also be used to infer macroscopic features of the characterized volume. Previous studies on the columnar-to-equiaxed transition have considered grains to be fully columnar when the primary aspect ratio was < 0.3 [46]. This group of columnar grains, with PAR < 0.3 are shown in Figure 5(a) and comprise 8.33% of the dataset volume. There are two main subgroups of these columnar grains: smaller grains that are approximately parallel to the build direction, and larger columnar grains that are inclined to the build direction. These smaller grains are located on both the left and right sides of Figure 5(a). The other subgroup of columnar grains are clustered together on the left side of Figure 5(a), which includes the previously characterized columnar grain shown in Figure 4. These larger columnar grains all have a similar angle of inclination to the build direction from the front to the back of dataset, which can be used to infer the heat source direction in this region. The largest grain in the characterized volume shown in Figure 3(b) is surrounded by these two groups of columnar grains (Figure 5(b)).

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Figure 5: The most columnar grains in the volume with PAR < 0.3 (a). The largest grain in the volume sits in middle of the various columnar grains (b). The angle of inclination of the larger columnar grains was used to determine the heat source direction. The central cluster (cluster ID 2) containing the nucleation orientation of the large grain as determined from K-means clustering analysis (c). The spatial distribution of misorientation using the improved nucleation orientation for the large grain (d). Misorientation increases from the bottom to the top of the grain as well as the front to to the back of the volume, along the solidification direction. IPF coloring is shown using the build direction as the reference direction. The most columnar grains are semi-transparent in (c) and (d) to enhance visibility of the important features of the large grain.

3.2.1. Cluster Analysis for Reference Orientation Identification Unlike the columnar grain shown in Figure 4, it is not straightforward to determine an initial nucleation orientation for the large grain due to its complex morphology. To determine a more suitable nucleation orientation for this grain, cluster analysis via the K-means algorithm was employed on the orientations contained within the large grain using the Python SciPy package [47]. The K-means algorithm segments data into a pre-selected number of clusters, choosing

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cluster centroids so as to minimize the intra-cluster variance given as the sum of squared distances (SSD) between each data point and its cluster’s centroid. The K-means algorithm can be expressed by Equation 2:

𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒 S

𝑘 ∑ ∑ 𝑖=1 𝑥∈𝑆𝑖

‖x − c𝑖 ‖ ‖ ‖

(2)

where c𝑖 is the centroid of the cluster of the set of points S𝑖 , k is the specified number of clusters, and x is an observation to be clustered. In the SciPy default implementation, centroids are iteratively calculated twenty times or until the SSD

as measured via Euclidean distance is not reduced by a threshold value of 10-5 , returning the centroid positions and point clusters resulting in the lowest measured SSD. As with calculation of average grain orientations, orientations in their as-collected state are not amenable to clustering operations due to symmetrically equivalent representations of a given orientation, so orientations were first placed into a symmetrically equivalent region of orientation space. Orientations were grouped without crossing a fundamental zone boundary to create a singular point cloud of data in orientation space. Although there are a variety of orientation spaces within which to work, the cubochoric representation was chosen for facile implementation of the SciPy package, which relies on Euclidean distance, and straightforward visualization of the orientation data in no more than three dimensions. The cubochoric representation is a three-component orientation space developed as an equal volume mapping of the homochoric ball to a cube, allowing for uniform sampling of all of orientation space with standard gridding approaches [48, 49]. Although cubochoric space is non-Euclidean (as is true of other orientation spaces such as Euler angle, homochoric, Rodrigues, etc.), Eulcidean distances in cubochoric space approximate Euclidean distances between unit quaternions for small misorientations, and Euclidean distance between unit quaternions is a valid metric on the set of 3D rotations (the group SO(3)) [50]. As the aim of the clustering analysis is to select an improved reference orientation for the large grain, the ease of implementation of cluster analysis via orientations in cubochoric space, as well as the distinct advantage of the space containing only three dimensions for direct visualization, outweighs any inaccuracies from the use of the Euclidean metric for clustering. K-means clustering was performed using 2 to 50 centroids to determine the optimal number of clusters for the orientations contained within the grain. The results of K-means clustering are shown in Figure 6. A simple derivative was calculated using the central difference method, and the elbow method [51] was then used to choose the optimal number of clusters as 6, which strikes the best balance between decreasing the SSD for the entire grain while still keeping the number of clusters low. The point cloud of orientations for the large grain in cubochoric space can be seen in Figure 7. This point cloud contains over 633,000 data points, and the results of K-means clustering with 6 clusters is shown in Figure 7(b). The K-means algorithm separates these orientations such that each of the 6 clusters occupies roughly the same volume of orientation space, but does not directly demonstrate the different densities of

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Figure 6: Results of K-means clustering algorithm from 𝑘 = 2 to 𝑘 = 50 clusters. The total intra-cluster variance as measured by the sum of squared distances between each point and its cluster’s centroid as a function of number of clusters 𝜕 𝑆𝑆𝐷 quickly decreases as the number of clusters is increased. The simple derivative 𝜕 𝑁𝑢𝑚𝑏𝑒𝑟 was calculated via the 𝑜𝑓 𝐶𝑙𝑢𝑠𝑡𝑒𝑟𝑠 central difference method and was used for the determining the optimal number of clusters using the elbow method. The optimal number of clusters was identified at 𝑘 = 6 when the derivative no longer changes significantly

the point cloud. Normalized values of the SSD for each cluster were calculated by dividing the SSD by the number of elements in the cluster. Comparison of the normalized SSD for each cluster to the size of the cluster is shown in Figure 8. Cluster ID 2 not only has the lowest normalized SSD, meaning it has the most compact cluster volume, but is also the largest cluster, containing 29.0% of all of the points in the grain. Cluster ID 2 is therefore the largest and most compact (least misoriented) cluster. We thus hypothesize that this grain likely contains the first part of the grain to solidify; a grain solidifying in free liquid has no reason to accumulate the large degree of misorientation observed in the bulk of the grain. This portion of the grain can be mapped back to its real-space location within the entire 3D dataset, and is shown in Figure 5(c). Cluster ID 2 not only forms the central portion of the large grain, but also contains the dendritic protuberances stretching from the right to the left side of the grain as shown in Figure 5(b). This projection also shows evidence of additional dendritic side-branching, indicating it solidified in a larger volume of free liquid and therefore earlier in the solidification process. Using the centroid of cluster ID 2 as a better approximation of the nucleation orientation results in calculated misorientations in the point cloud as shown in Figure 7(c). Misorientations can be seen to increase away

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Figure 7: Point cloud of all orientations of the largest grain in the characterized 3D volume shown in cubochoric space. IPF color representation using the build direction as the reference direction (a). Clusters identified using K-means with 6 clusters (b). Calculated misorientations using the centroid of cluster ID 2 as the reference orientation (c). This orientation was selected as an improved nucleation orientation for the grain. The entire point cloud contains over 633,000 points.

Figure 8: Properties of clusters determined by K-means algorithm for 𝑘 = 6 clusters. Clusters with lower normalized values of the sum of squared distances (SSD) occupy less volume in orientation space. Cluster ID 2 has both the lowest normalized SSD and largest fraction of data, making it the densest and least misoriented cluster.

from the nucleation orientation to both ends of the point cloud. When these misorientations are again mapped back to the sample-space, similar behavior is observed in the large grain as was seen in the columnar grain shown in Figure 4. Misorientations increase from the bottom to the top of the grain, as well as along the heat source direction, following the expected solidification direction for this grain.

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3.3. Chemical Analysis of Solidified Microstructure

The large grain was not fully removed during laser ablation, and the complex morphology of this grain results in

a surface that contains portions that are highly misoriented from each other. Energy-dispersive X-ray spectroscopy (EDS) was conducted on a portion of the remaining surface as shown Figure 9. Both manganese and silicon are found to be enriched in the upper portion of the grain and depleted in the lower portion of the grain, indicative of chemical segregation occurring during solidification. The relative rejection or accumulation of solute elements in an alloy during solidification is characterized by the partition coefficient, which by convention is less than unity for elements that are rejected into the liquid during solidification, and greater than unity for elements that accumulate in the solid during solidification. The higher the deviation from unity for the partition coefficient, the stronger the partitioning of that element during solidification. For the composition of the alloy given in Table 1, the most strongly segregating elements with sufficient concentration to be readily detected via EDS are manganese and silicon, both of which should preferentially segregate to the liquid. For stainless steels, partition coefficients for Mn and Si are in the range of 0.7 and 0.5, respectively [52, 53]. The upper portion of the grain (magenta IPF coloring), therefore, should be expected to have solidified later than the lower (tan/peach IPF coloring) portion of the grain.

4. Discussion TriBeam tomography is one of several 3D characterization approaches that provide rich crystallographic and structural information on volumes of material on the scale of hundreds of microns to a millimeter in extent. TriBeam tomography is inherently a destructive characterization technique, similar to other sectioning approaches such as mechanical serial sectioning [54, 55]. Non-destructive techniques commonly employ high energy X-rays at synchrotron facilities, including diffraction contrast tomography (DCT) [56] and high energy x-ray diffraction microscopy (HEDM) [57]. Longitudinal studies of samples across multiple characterization approaches have shown good agreement in terms of grain morphology between DCT and HEDM, with differences in grain volume on the order of 10% or less and DCT exhibiting poorer angular resolution of orientations than HEDM in a deformed sample [58]. Comparison of DCT to TriBeam tomography has shown higher spatial resolution is attainable using the serial sectioning technique, particularly at grain boundaries, enabling identification of smaller grains both within the sample bulk and at the sample surface [59]. The destructive nature of serial sectioning techniques, however, precludes their use in four-dimensional experiments.

4.1. Interpretation of Cross-sections using 3D Data

Full 3D characterization of as-built additive samples allows for more comprehensive interpretation of the complex

solidification microstructures that develop in this process. Particularly for additive microstructures, conventional 2D

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metallographic cross-sections can be hard to interpret independently. Two perpendicular cross sections of the stainless steel LENS sample, with plane normal either parallel to the build direction (transverse cross-section) or perpendicular to the build direction (frontal cross-section), are shown in Figure 10. Both of these EBSD scans were collected using a square grid with a step size of 3 µm, identical to the resolution used for 3D characterization. The transverse crosssection (Figure 10(a)) shows what appear to be more equiaxed grains in between regions of larger chevron shapes. In typical weld microstructures, columnar grains begin at the edges of melt pool and depending on welding conditions, equiaxed grains may form along the center line of the weld [60]. In the frontal cross-section (Figure 10(b)), the scalloped shape of prior melt pool boundaries are visible, resulting from hatches deposited from the right to the left of the micrograph. The frontal cross-section alone is insufficient to determine whether the heat source was travelling into or out of the plane for each deposited hatch. The 3D characterization not only allowed for direct determination of the heat source direction for the characterized volume, but also allows for more accurate interpretation of these cross-sections. The grains appearing as roughly equiaxed in the regions between the chevron shapes in the transverse cross-section are in fact the columnar grains shown in Figure 5(a) that are well aligned with the build direction. These grains lie along the center-line of the deposited hatch and thus grow nearly vertically with respect to the build direction along the direction of maximal thermal gradient. The chevron shapes, however, lie near melt pool boundaries, and are partially remelted on the subsequent deposit, altering the original growth direction of the grains. A major cause of the complexity of the observed microstructures arises from the large degree of hatch overlap (∼40%) used in the production of the sample, resulting in the middle of one deposited hatch becoming the edge of the adjacent melt pool. In the 3D volume, the two groups of smaller columnar grains that are well-aligned with the build direction comprise the center-line of two adjacent hatches. The 3D volume sampled in this study has fully characterized the remelted region between adjacent hatches that arise from a large hatch overlap. The larger columnar grains on the left side of Figure 5(a), which are not well-aligned with the build direction, are growing along the heat source direction toward the center-line of the hatch deposited after that on the right side of 3D volume. The large grain analyzed via the K-means algorithm likely began as a columnar grain near the center-line of the hatch deposited first, but was remelted on the adjacent hatch. This explains the large dendritic projection of the grain, arising due to remelting of some of the original grain, with the final grain persisting on both sides of the remaining melt pool boundary. The remelting process can account for the complexity of the shape of many of the larger grains observed in this 3D dataset. For example, the chevron shapes observed in the transverse cross-section (Figure 10(a)) are a result of remelted grains changing growth direction due to the bi-directional raster scan strategy used during part manufacture. The effects of remelting can also be observed in the frontal cross-section (Figure 10(b)), where grains crossing remaining melt pool boundaries can be seen to change direction by as much as 90°. This effect has been observed in other DED processes, in which bi-directional scan strategies that do not rotate 90° between layers (cross-hatching) perpetuate the continual AT Polonsky et al.: Revised article submission for Acta Materialia

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growth of large grains that grow in a zig-zag pattern along the build direction [29]. A bi-directional scan strategy with cross-hatching between build layers helps to prevent the persistence of grains across many build layers, but remelting and regrowth of grains across melt pool boundaries still occurs within individual build layers.

4.2. Misorientation Accumulation

The effect of grain remelting on final grain size and morphology make the hatch spacing in the LENS process a

key process variable for controlling the as-deposited microstructure. A larger hatch spacing can result in less remelting between adjacent hatches, creating melt pool boundaries that more closely resemble the idealized half-ellipsoidal melt pool shape [32, 61, 62]. Although individual grain morphology may become less complex as hatch overlap is reduced, LENS-manufactured materials are still highly anisotropic in their as-deposited state and contain grains with large orientation gradients [21, 63]. For both the columnar grain and the large grain analyzed in section 3, determination of the location where the grain first nucleated and using this as a reference location and orientation demonstrated that misorientation increases along the growth direction of each grain. Rather than having an even and random distribution, large degrees of misorientation appear to be concentrated in the last parts of the grain to solidify. As shown in Figure 3, larger grains tend to have larger degrees of misorientation, potentially due to longer total solidification times, but also due to remelting. As misorientation within a grain requires some physical deformation the crystal, it is likely that this occurs in the solid state just after the last liquid freezes and accommodates shrinkage in the liquid; the flow stress of the material is expected to be extremely low at these temperatures.

4.2.1. Scheil-Gulliver Analysis If misorientations are assumed to increase as solidification progresses, their distribution should qualitatively capture the thermal and solutal path of the solidification process. The Scheil-Gulliver equation captures the changing composition of both the solid and liquid during the solidification process. Due to the sloping solidus and liquidus surfaces, some alloying elements will preferentially be rejected to the liquid or accumulated in the solid as the alloy solidifies. To investigate this relationship for the 304L stainless steel of this study, a Scheil simulation was conducted in Thermocalc using the full chemical composition provided in Table 1 and calculated using the TCFE7 Database with a step increment of 1° Celsius. ?? shows the results of the Scheil simulation in conjunction with the misorientations

extracted with consideration of the nucleation orientation determined for both the columnar and the large grain in section 3. When the misorientations are simply ranked in increasing order, both distributions show qualitatively similar behavior. Both of these grains are sufficiently large for this relationship to be statistically significant. The columnar grain in ??(a) contains over 19,000 voxels, while the large grain in ??(b) contains over 633,000 voxels. The selection of the proper nucleation orientation is critical to this analysis. When a different cluster centroid is chosen from the Kmeans analysis of the large grain, much higher misorientations can be measured, up to 17°. However, the distribution

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of misorientations using these other reference orientations does not at all correlate with the temperature distribution determined from the Scheil simulation. Using the relationship between misorientation and fraction solid for the large grain as shown in ??(b), the lower portion of the large grain shown in Figure 9(a) with tan/peach IPF coloring solidified

at ∼0.4 fraction solid, whereas the upper portion of the grain with magenta IPF coloring solidified at the very end of solidification, at ∼0.99 fraction solid. The distribution of manganese and silicon as determined from EDS of the region is consistent with this characterization, with the lower portion of the grain being depleted in these solute elements, and the upper portion of the grain being enriched in these solute elements. The Scheil analysis does not consider any of the complex fluid flow phenomena that occur during the LENS process, but given the solute enrichment patterns observed here, fluid flow may be an important factor in determining the final distribution of solute and misorientation.

4.2.2. Location Dependence of Intra-Grain Misorientation Although segregation, as measured here, occurs at the scale of individual grains as they solidify, it does not fully account for the variation in misorientation that occurs on a grain to grain basis. Segregation does, however, control the solidification pathway of the material, namely the rate at which solid will form as heat is extracted through the base metal during these welding processes. The Scheil simulation shows that over the early stages of cooling, the fraction solid rapidly changes from 10% to 80%. Beyond this, much of the melt pool has solidified and grains are largely constrained by their surrounding neighbors. There is no longer ample free liquid that can allow large projections and

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dendritic branches to form as with the portion of the large grain shown in Figure 5(c). As solidification approaches its endpoint, and the grains become more and more constrained, so too does the liquid temperature start to rapidly decrease. Nearly 80% of the freezing range is traversed for only the last 5% of solid to form. As the liquid cools, it contracts, creating tensile stresses on the solidifying grains. As the grains are no longer able to move freely in the liquid, constrained by the rest of the solidifying melt pool, these stresses plastically deform the grains, creating changes in orientation. This process is exacerbated by the reduced yield strength of the material so close to its melting point [64]. Such solidification behavior is also linked to hot tearing of alloys, of which additive processes are not immune, wherein interdendritic films trapped at the end of solidification create isolated regions of high stress, deforming the semi-solid matrix and initiating cracks [65, 66]. These cracks tend to form near the last solid to form near the centerline of the melt pool, where these thermal effects are strongest. Other models have directly related the rate of change of temperature as the solid fraction increases to the solidification cracking susceptibility [67]. The end of solidification has been linked to larger changes in temperature and higher cracking susceptibility as longer interdendritic channels become harder to feed with free liquid. Such approaches couple the thermal and solutal contributions to cracking phenomena beyond the primarily mechanical arguments of the RDG model [65] and predictions of segregation from Scheil simulations. Thus characterization of the orientation gradients in the manner shown here permits a better understanding of the crack "precursors" and their relationship to alloy composition. In conjunction with the spatial distribution of misorientation in both grains, which also follows their solidification direction, misorientations can be seen to accumulate within individual grains as solidification progresses. This entire process is controlled by the chemistry of the alloy; the changing chemical composition during solidification at the solid/liquid interface controls the local liquidus temperature and speed of the interface. The misorientations found in both the large grain and the columnar grain follow the trend of the Scheil curve, particularly at the late stages of solidification, at fractions of solid >80%. The large grain exhibits higher misorientations at earlier stages (over larger fractions of the volume of the grain) due to the re-solidification process induced by the overlap. For grains in the remelted portion of the melt pool, grain morphology becomes more complex as the direction of maximal thermal gradient changes direction, increasing not only grain size but providing an additional opportunity to accumulate higher misorientations within individual grains. This process is shown schematically in ??, wherein the deposition of an

adjacent hatch creates the complex grain morphologies and large misorientations observed in the LENS material. When the primary weld bead is deposited, grains grow along the direction of maximal thermal gradient, toward the center of the melt pool. Some grains are out-competed by more favorably oriented grains, resulting in a range of ultimate grain size. Thermal and solutal effects lead to the accumulation of misorientation as solidification progresses,

as shown with the columnar grain in ??(a). When the subsequent weld bead is deposited, some grains crossing the

melt pool boundary persist, re-solidifying with the orientation at the melt pool boundary, but along a new direction of AT Polonsky et al.: Revised article submission for Acta Materialia

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max thermal gradient. These grains exhibit the grain shape as shown in ??(b), accumulating additional misorientation

during the second solidification event.

4.3. Implications for Additive Components

The correlation between thermal and solutal effects with misorientation in these as-deposited microstructures has

important implications for additive manufacturing processes. Although the grain morphology and texture of these materials can be made to resemble that of conventionally wrought material via recrystallization, these heat treatments are generally not sufficient to fully chemically homogenize the material, so any segregation occurring on a grain level during processing will remain after heat treatment. This segregation on a grain level could explain the differing mechanical behavior between wrought and recrystallized LENS samples of stainless steels when subjected to high strain rate loads, as well as the inferior fatigue performance of many additively manufactured materials, even after a hot isostatic pressing (HIP) heat treatment [37, 68–70]. Segregation arising during the AM process may also the explain variable corrosion resistance observed in these materials, where chemical and microstructural heterogeneity can create pockets of higher corrosion activity [71, 72]. Localization of misorientation within an as-deposited structure may also contribute to stress concentrations, leading to crack initiation, decreasing effective lifetimes of parts and inferior macroscopic yield behavior. Non-uniform distributions of misorientation and residual stress in additive parts can also lead to differing recrystallization behavior as compared to wrought and deformed materials, with incomplete recrystallization observed in some cases, as well as higher temperatures and longer times necessary to achieve complete recrystallization [73, 74].

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The accumulation of misorientation may be possible to mitigate via control of the solidification process during AM. Modifications to traditional alloy compositions can be aimed to minimize or decrease the amount of liquid that persists to low temperatures due to solute segregation. This provides a potential design pathway for new alloys, more amenable to the unique challenges of additive manufacturing. Such insights are enabled by advanced characterization approaches, such as TriBeam tomography, and are essential to understanding microstructure development in additive processes for improved performance, reliability, and predictability of additive parts.

5. Conclusions TriBeam tomography of LENS-processed 304L stainless steel has characterized the complex grain morphology and large orientation gradients within the as-deposited material. Full 3D characterization can be used to more accurately interpret the highly anisotropic microstructures observed in conventional 2D cross-sections of these materials. Complex grain morphologies were linked to the remelting of adjacent deposits during the manufacturing process. Orientation gradients were analyzed in terms of progression from the original point of grain nucleation, which offers an advantage over average grain orientations via incorporation of details of the manufacturing process. For complex grain morphologies, K-means cluster analysis was useful in determining the original location and orientation of the nucleated grain. Misorientations were found to increase along the direction of solidification of these grains. Within individual grains, the evolution of misorientation followed the evolution of fraction solid (and local solute composition) as predicted by a Scheil analysis. The presence of Scheil effects was confirmed via solute segregation measurement at the scale of a single grain.

6. Acknowledgements This work was supported by the National Nuclear Security Administration Grant No. DE-NA 0002910 and by the Department of Defense Vannevar Bush Fellowship Grant No. ONR N00014-18-1-3031.

7. Conflicts of Interest On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Figure 9: Postmortem analysis of segregation within the large grain. IPF coloring (a) and calculated misorientation (b) for the large grain from 3D characterization. Despite the large change in IPF coloring observed in (a), the entire displayed area is for the single large grain shown in Figure 5. EDS maps for both Mn (c) and Si (d) showing relative abundance of these elements from average measured intensity. EDS maps were taken of the same selected area shown in (a) and (b). Both Mn and Si have partition coefficients < 1, so will segregate to the liquid during solidification and enrich the last liquid to solidify. Mn and Si are found to be enriched in the more highly misoriented region of the large grain, which is consistent with this portion of the grain solidifying after the lower portion.

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Figure 10: 2D EBSD maps of the as-deposited 304L sample. Taking the build direction as the vertical axis of the sample, microstructures viewed in both transverse (a) and frontal (b) cross-section show the complex grain morphology arising from manufacture. The location of remelted and columnar grains for multiple deposits is marked in the transverse slice (a). Remaining melt pool boundaries are outlined in the frontal slice (b), with subsequent tracks being deposited from the right to the left of the imaged area.

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Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: