1 Introduction

In recent years, metal additive manufacturing (AM) has gained increasing attention from both industry and research communities.[1,2] Laser powder bed fusion (L-PBF) has emerged as a prominent AM technology[3,4] and has been used to manufacture components of many alloys.[5,6] Recent extensive research has demonstrated that stainless steel samples manufactured through L-PBF, with optimized printing parameters, exhibit many superior mechanical properties compared to their cast and wrought counterparts.[7,8] Given that almost fully dense samples can now be printed,[9] an in-depth understanding of microstructural characteristics is of particular importance, as the microstructure is the vital link connecting the processing to the resulting material properties.

The L-PBF process introduces a distinctive microstructure. Taking steel as an example, it is widely recognized that L-PBF leads to a hierarchical microstructure.[7] Notably, the sub-grain scale feature known as the ‘cell structure’ has gained significant interest in recent work.[10,11,12,13,14,15,16] Certain studies have attributed the enhanced mechanical properties of L-PBF metals to this distinct additive-manufacturing-induced cell structure.[17,18] The literature, however, reports different cell structure morphologies and the nomenclature for grains and cells are even sometimes confused. Some studies mixed these two terms probably because they share many microstructural characteristics, e.g., epitaxial growth. Furthermore, the cell size has been used to predict yield strength of AM steels[19,20] by the Hall–Petch relationship, which strictly speaking is proposed for grains. Part of the explanation for the confusion may be that the description of the cell structure has been based on 2D investigations, and the terminology from conventional welding studies was applied, e.g., dendritic and cellular.[14] Even though AM and welding share similarities, this is not an accurate approach, considering that the cells undergo a much more complex thermal history during AM compared to welding. Recently, the most common belief is that cells in AM samples have a 3D tube-like morphology with honeycomb sections.[14,21,22] However, direct 3D imaging of the cell morphology is to the authors’ knowledge not reported in the literature. Moreover, the formation mechanism of cell structure is not agreed upon yet and a fundamental understanding is critical for controlling the microstructure and properties of AM metals.

This study aims to quantify the 3D morphology of the AM-induced cell structure. We achieve this by introducing an edge sample, which allows us to reconstruct the 3D morphology from two perpendicular sections of the sample. We also discuss the formation mechanism of the cell structure and relate the theories to our experimental results. A common AM alloy, namely austenitic stainless steel 316L, is used in this work.

2 Experiments

A cubic sample of stainless steel 316L, measuring 10 × 10 × 10 mm3 in size, was printed. The printing was carried out utilizing a custom-built open-architecture and open-source L-PBF system (the complete source is available at https://github.com/DTU-OpenAM/OpenAM-PBF, released in January 2024), which operates as a production machine while allowing comprehensive experimental flexibility. Its subsystems were either crafted in-house or acquired to manage processes through conventional interfaces and modular configurations.[9] The powder employed was standard 316L powder, and its chemical composition is given in Table I. The supplier provided the following particle size distribution information: D10 = 25.1 µm, D50 = 41.3 µm, and D90 = 64.8 µm.

Table I Chemical Composition of the Powder as Provided by the Supplier Höganäs in Wt Pct
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Standard parameters that were previously optimized to produce near fully dense components (<0.2 pct porosity) were utilized in the present work: laser power P = 250 W, scanning speed s = 650 mm/s, layer thickness t = 50 µm, and hatch distance h = 100 µm, resulting in a volume energy density VED = 76.9 J/mm3.[9] After each layer, the scanning direction was rotated 90°. To analyze the origin of the cell structure, after printing the cube, several single tracks were printed on the top of the printed cube, as shown in Figure 1(a). The printing parameters of the single tracks were the same as those of the cube sample. The printing was done in a nitrogen atmosphere and the oxygen content throughout the print was < 1000 ppm.

Fig. 1
figure 1

(a) Schematic diagram of the edge sample, where two perpendicular interior sections were prepared for examination. (b) SEM images of the edge sample, combining the two sides of the edge aligned by melt pool boundaries and showing (i) in 2D, three types of cell morphologies: equiaxed, extended, and columnar, and (ii) in 3D, a prism-like cell morphology. (c) through (d) Schematic diagrams of the 3D prism-like morphology of cells, which matches the morphology shown in the red boxes in (b). Colored coordinate systems are added to ease the understanding (Color figure online)

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To analyze the 3D morphology of the cell structure, an ‘edge sample’ was prepared from a position close to the center of the printed cube for examination by scanning electron microscopy (SEM) in a Zeiss Sigma 300 microscope equipped with an electron backscatter diffraction (EBSD) detector from Oxford Instruments. As shown in Figure 1(a), the approach involved cutting the bulk sample into four pieces, allowing for inspection of an internal zone exhibiting stable printing. Subsequently, two surfaces perpendicular to each other were prepared by grinding with SiC papers and polishing with diamond suspensions, followed by final polishing using a colloidal silica suspension (0.04 µm). To reveal the cell structure, the prepared sample was etched using a solution with HF: HNO3: H2O = 2:8:90. Both prepared surfaces, including the edge area and the single-track area, were examined by SEM and EBSD at an acceleration voltage of 20 kV. EBSD maps were obtained using a step size of 30 nm. Gentle noise reduction, e.g., removing wild spikes and filling zero solutions with neighbor orientations, was applied using the AZtecCrystal software.

For a more detailed observation of the dislocation characteristics, a transmission electron microscopy (TEM) specimen was cut out from the cubic sample, as shown in Figure 1(a), and was prepared through twin-jetting using a 10 pct perchloric acid solution by Struers TenuPol-5 at a temperature of − 25 °C.[23] A JEOL JEM-2100 microscope was used for the characterization at an acceleration voltage of 200 kV. High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) and energy-dispersive X-ray spectroscopy (EDS) were applied to characterize the segregation at cell walls. To detect weak segregation, a high beam current and a long scanning period of more than 1 hour were used.

To gain insight of the segregation phenomenon of L-PBF 316L, a simulation was done in Thermo-Calc 2024a using the TCFE12 and MOBFE7 databases, the nominal chemical composition of 316L, and the printing parameters applied in this work. Segregation during solidification was calculated using the Scheil model with solute trapping. The final chemical composition after liquid–solid transformation was used in the ‘Homogenization module’ to calculate homogenization during cooling from the solidus temperature to 600 °C. A cylindrical geometry with an average diameter of 0.6 µm was used in the simulation, to match as closely as possible the experimental situation.

3 Results

3.1 The 2D/3D Morphology of Cell Structure

Figures 1(b) through (d) show the cell structure morphology seen from both sides of the edge sample. The image is a combination of the two perpendicular sections aligned by the help of melt pool boundaries. The image clearly reveals why diverse results are obtained when only 2D sample sections are inspected. In 2D, three distinct types of cell structure morphologies are readily discernible, each forming a cell group (CG) with boundaries defined by either melt pool boundaries or grain boundaries. The three types are as follows:

  • Equiaxed cells. These cells possess a polygonal shape, typically appearing as pentagons or hexagons, depending on the number of adjacent cells. Their sizes vary across different regions. Larger equiaxed cells have an equivalent diameter of approximately 0.8 µm, whereas smaller ones measure only about 0.4 µm.

  • Extended cells. Similar in shape to equiaxed cells, however, elongated in a specific direction. In Figure 1(b), the extended cells are elongated along the building direction. Consequently, the size of extended cells varies depending on the direction of measurement: perpendicular to the extension axis, their dimensions resemble those of equiaxed cells, while along the extension axis, they may exceed 1 µm in size.

  • Columnar cells. These cells appear as parallel lines in 2D. They typically reach from one melt pool boundary, or grain boundary, to another. The spacing between each line also varies across different regions.

As illustrated in Figures 1(b) through (c), the center region of the image exhibits a clear transition from a typical columnar morphology on the left side to equiaxed morphology on the right side. Multiple locations along the edge of the edge sample show similar characteristics, such as a pair of horizontal columnar cells and equiaxed cells, or a pair of inclined columnar cells and extended cells, as illustrated in Figure 9 in the appendix. It is thus clear that the cell possesses a 3D morphology similar to a collection of slender n-gonal prisms, each having a polygonal cross section and an equivalent diameter of less than 1 µm. These prisms exhibit various spatial orientations, and the observed 2D morphology is a consequence of their intersection with the observation plane. While a similar suggestion has been made previously based only on 2D observations,[21,22] the present usage of the edge sample provides the direct evidence to support the 3D prism-like morphology hypothesis. As shown in Figure 2, detailed EBSD characterization of the edge sample furthermore reveals that all the observed cells have their long axes oriented along one of the < 001 > crystallographic directions, which corresponds to the preferred growth direction for Face-Centered Cubic (FCC) crystals.[24] This further supports the 3D prism-like morphology hypothesis.

Fig. 2
figure 2

An overlay of SEM images of the edge sample and the related IPF coloring maps. The red cubes (visualizing the crystal orientations) and 3D prisms (visualizing the prism-like cell morphology) indicate that the cells have their long axes oriented along one of the < 001 > crystallographic directions. Colored coordinate systems (see Figure 1(a)) are added to ease the understanding (Color figure online)

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As shown in Figure 3, the TEM bright-field images illustrate all three types of 2D cell morphologies. It is clear that the dislocation density within the cell walls is high. The misorientation angles across these cell walls were determined by Kikuchi patterns, revealing remarkably low values, with misorientation angles around 0.5°. Within the cell interior, dislocations are more loosely distributed but still exhibit a discernible pattern: dislocations appear to separate the prism cells into distinct segments, resulting in a bamboo-like dislocation structure. In other words, within prism cells, there are also loose dislocation boundaries which are invisible in SEM images. Additionally, TEM images reveal randomly distributed nano-scale-sized spherical particles.

Fig. 3
figure 3

TEM images: (a) equiaxed cells, (b) columnar cells within two grains, and (c) extended cells. Cell walls and cell interiors are observed with different dislocation densities: dislocations are highly entangled at cell walls, and are loosely distributed within the cell interior, forming a bamboo-like dislocation structure

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3.2 Side-Branching Phenomena

3D side-branching is another significant observation, see Figure 4. The concept of side-branching describes that when a preferred growth direction, such as one of the < 001 > directions for FCC crystals, is aligned with the thermal gradient, then the cell axis is parallel to this direction. However, when the thermal gradient deviates from this preferred direction, the cell axis may rotate by 90° to realign with a different < 001 > direction that is closer to the thermal gradient.[25] Our results are in good agreement with literature,[25] and further extends the side-branching concept from 2D to 3D, as illustrated in Figure 4. In Figure 4(a), three cell groups with very small misorientation angles display three different morphologies, each aligned with one of the < 001 > directions, clearly documenting the occurrence of 3D side-branching. The misorientation angles across the melt pool boundaries (yellow dashed lines) and grain boundaries (red dashed lines) are given in Figure 4(a). Figure 4(b) illustrates that, when side-branching occurs, the prism-like cells undergo a smooth 90° turn.

Fig. 4
figure 4

The occurrence of 3D side-branching. (a) SEM image with overlaid IPF coloring map: three CGs have nearly the same crystallographic orientation but different cell morphologies. The dashed lines indicate melt pool boundaries (yellow) and grain boundaries (red), surrounding the CGs. The misorientation angles across these boundaries are marked. (b) TEM image illustrates a smooth 90° turn when side-branching occurs (Color figure online)

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A more complete sketch of the AM microstructure is shown in Figure 5. It shows melt pools within three layers, each rotated 90°. The direction of the thermal gradient is highly influenced by both the geometry of melt pool and scanning speed. The zoom-in image in the black box illustrates how 3D side-branching occurs near the melt pool boundary intersection. It is believed that the side-branching phenomena are more likely to occur in the intersection of melt pool boundaries, as the direction of the thermal gradient undergoes a significant change in this area, due to the sequence of melting and solidification. Normally, with optimized printing parameters and sieved powder, i.e., no unmelt powder or impurities, the cells prefer to epitaxially grow with or without side-branching, as it requires lower energy. Therefore, if none of the three < 100 > directions align close to the thermal gradient, the growth may slow down, and the growth front may be impinged by other cell groups growing from a different angle.

Fig. 5
figure 5

Schematic illustration of the AM microstructure. The sketch shows melt pools within three layers. The building direction, scanning direction, laser beam moving direction, thermal gradients, and crystallography direction are indicated by colored arrows. The sketch in the black box is a zoom-in image of a region near a melt pool boundary intersection, showing 3D side-branching with cells aligned along the local thermal gradient. The scanning direction for each layer is shown in brackets (Color figure online)

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4 Discussions

4.1 The Formation Mechanism of Cell Structures

In the L-PBF process, three distinct stages emerge: liquid–solid transformation, cooling, and subsequent thermal cycles. The cell structure can potentially start to form during any of these stages and evolve during the following stages. There are several hypotheses regarding the origin of the cell structure developed upon L-PBF.[15,26,27] The present results suggest that the formation of cell structure in L-PBF 316L is a combined effect, which is discussed below.

4.1.1 Liquid–Solid Transformation Stage

Early studies proposed that the formation of the cell structure occurs during the liquid–solid transformation, and the morphology of the cells depends on the ratio of the thermal gradient G and the solidification rate R.[26] With a decreasing ratio of G/R from a melt pool boundary towards the melt pool center, the cell morphology changes from columnar to equiaxed. Solute segregation and/or a high density of nano-particles, which are usually observed at the solidification boundaries,[7,14] act as a spatial framework pinning dislocations during the cooling process, thus forming the cell structure. This hypothesis is similar to the conventional solidification cell formation mechanism. According to the solidification theory, solidification cells form at high cooling rates, due to solute redistribution in combination with the surface energy that stabilizes the surface of the growing crystal at high growth velocities to ‘cancel out’ secondary arms on the growing crystals.[28,29,30] These solidification cells are usually ellipsoid-like crystals that grow anti-parallel to the heat flux direction. Notably, microsegregation is typically considered as a prerequisite for solidification cell formation.[31,32,33]

For AM samples, however, microsegregation is not always observed.[8,34] Our simulation, as shown in Figure 6(a) through (b), shows that, for L-PBF 316L, at the beginning of cooling, i.e., at the end of liquid–solid transformation, chromium (Cr) and molybdenum (Mo) are strongly segregated at the cell walls. However, after a very short time (0.1 second), the segregation becomes weak, and after 1 second, almost no segregation is present. In this work, we used STEM-EDS to detect this very weak segregation by using a long mapping time of more than 1 hour. The results are shown in Figure 6(c) through (f), indicating a week segregation, as is especially clear from the line profile. Thus, during the liquid–solid transformation of 316L, segregation occurs but may diminish after a very short time due to a high equilibrium partition coefficient of these elements.[35,36] This solute segregation, albeit very weak, coincides with the final dislocation cell structure, and thus may be the first step of cell formation. Furthermore, during the epitaxial growth of the prism-like cells, the initial crystallographic orientations of neighboring cells might be slightly different due to the slight variation of the crystallographic orientation they inherit, and therefore a dislocation network may already be present to accommodate the small misorientation between neighboring cells before the material cools down.

Fig. 6
figure 6

Simulation results show that (a) Cr and (b) Mo were strongly segregated immediately after the liquid–solid transformation, but this segregation diminishes during cooling. The x-axes in (a) and (b) represent the radial distance from the center of a cell to the edge of a cell. The solidification process proceeds from the cell center to the cell wall. The simulations were performed at a cooling rate of 155 °C/s from the solidus temperature during the first 5 s. STEM-EDS was used to detect this weak segregation using a very long scanning period: (c) HAADF image, (d) through (e) Cr and Mo mapping, and (f) Cr and Mo line profile

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4.1.2 Cooling Stage

An alternative hypothesis suggests that the formation of cell structure occurs during cooling, driven by thermal deformation.[15,27] According to this view, the solidified material acts as a constraint, generating thermal stress. This stress, coupled with a relatively high dislocation mobility of the material at high temperature, leads to plastic deformation and cell formation.[37,38,39] The importance of thermal deformation has gained prominence in recent years, with supportive indications from simulations.[40,41] This process may appear rather similar to the development of deformation cells in conventional manufacturing: for many alloys, conventional plastic deformation gives rise to a 3D dislocation structure, termed deformation cells here. The morphology of the deformation cell structure is controlled by the grain orientation with respect to the deformation axis.[42] The deformation cells are characterized by cell walls with high dislocation densities, while the regions between the walls exhibit a relatively lower dislocation density.[42,43,44,45]

Plastic deformation of FCC metals through wavy glide gives rise to an equiaxed deformation cell structure as well as planar dislocation boundaries, depending on the loading direction and the grain orientation.[42] In the present work, the cells have been found to have a prism-like morphology with an internal bamboo substructure. The prism-like cell walls coincide with the segregation network formed during liquid–solid transformation. This 3D morphology, which is significantly different from that formed during conventional plastic deformation, suggests that the dislocations created by the thermal strain are mostly deposited on the initial segregation/dislocation network, whereas additional dislocations form the internal bamboo substructure by mutual trapping, similar to the formation of incidental dislocation boundaries during plastic deformation.[46] The initial segregation/dislocation network provides a preferred location for the formation of the cell boundaries, while the cell boundaries may in return also stabilize the segregation network, i.e., becoming more stable than the simulation, shown in Figure 6, predicts.

4.1.3 Subsequent Thermal Cycles

The third hypothesis proposes that subsequent thermal cycles, inherent to L-PBF, also have an impact on cell structure. This intrinsic heat treatment will induce thermal expansion and shrinkage, which may lead to cell formation. A recent work utilizing synchrotron X-ray techniques revealed that subsequent thermal cycles indeed affect the dislocation structure evolution.[45]

As shown in Figures 7(a) though (d), SEM images of our single-track 316L sample reveal that, even without such thermal cycles from both adjacent tracks and subsequent layers, the segregation network exists. The morphology of cells in the single track is similar to the one in the bulk interior (see Figure 1). The KAM map, shown in Figure 7(e), however, qualitatively suggests a higher dislocation density in the bulk interior than in the single-track part. This implies that the thermal cycles introduce extra dislocations and contribute to the formation of the final dislocation cell structure.

Fig. 7
figure 7

(a) SEM image of a single-track 316L sample, showing three types of 2D cell morphology: (b) equiaxed, (c) extended, and (d) columnar. (e) KAM map qualitatively showing the increasing dislocation density from the single track to the bulk interior

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It follows that during L-PBF, the rapid liquid–solid transformation leads to the formation of an initial prism-like cell structure (segregation/dislocation network). The final as-printed cell structure, including cell walls with high-density dislocations and loose dislocation boundaries inside the cells, is eventually formed by the thermal strain from the cooling and the subsequent thermal cycles.

4.2 Strengthening Mechanisms

L-PBF 316L have superior tensile properties compared to their conventionally manufactured counterparts.[47,48,49] Figure 8 summarizes some of the yield strength and elongation reported in the literature. In general, the as-printed samples can achieve a yield strength of 500–600 MPa with an elongation of 40–60 pct. For comparison, conventionally manufactured 316L samples typically have yield strengths between 200 and 350 MPa with an average uniform elongation of 50 pct.[50,51,52,53]

Fig. 8
figure 8

Summary of tensile properties of L-PBF stainless steel 316L reported in the literature

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Many studies attribute the enhanced tensile properties to the cell structure.[17] However, the detailed strengthening mechanisms are still unclear, and all of the following strength contributors may play a role: solid solution strengthening, particle strengthening, grain boundary strengthening, and dislocation strengthening.[8]

Solid solution strengthening can be estimated by Ref.[54]:

$${\Delta \sigma }_{ss}=\sum_{i=1}^{n}{K}_{i}\times {C}_{i},$$

where \({K}_{i}\) is the strengthening coefficient for each solute element i, and \({C}_{i}\) is the concentration of solute element i. Based on the \({K}_{i}\) values taken from the literature and the nominal chemical composition from Table I, the contribution from solid solution strengthening is calculated to be about 150 MPa. The contribution from solid solution strengthening is expected to be similar for L-PBF 316L and conventionally manufactured 316L, as they have the same nominal chemical composition and the segregation in L-PBF samples is very weak.

Particle strengthening is important for some alloys, such as maraging steels, because they tend to form precipitates after aging treatments.[55] For conventionally manufactured 316L, particles are negligible and do not affect the strength; for L-PBF 316L, we found randomly distributed particles within the sample and nano-particles located at the cell walls.[56] These particles occupy a very small volume fraction and are relatively stable during annealing.[57] By comparing conventionally manufactured 316L and fully recrystallized L-PBF 316L with similar grain sizes, it is found that their yield strengths are comparable and around 300 MPa.[58,59] This indicates that particle strengthening is not significant for L-PBF 316L. Calculations based on Orowan strengthening suggest that the maximum contribution of particles to the yield strength is about 37 MPa.[8]

It is well known that L-PBF leads to a columnar grain structure and therefore results in mechanical anisotropy: when the tensile axis is parallel to the building direction, the sample shows a higher yield strength than when perpendicular.[60] According to the results shown in Section III.B, epitaxial growth with side-branching often occurs at the intersection of several melt pool boundaries. During solidification, grains can, due to side-branching, grow along three perpendicular directions to best match the local thermal gradient. As a result, grains can grow to a large size, crossing several melt pool boundaries. This may also affect the grain aspect ratio depending on the building condition. According to the Hall–Petch relationship, side-branching reduces grain boundary strengthening. It is reported that the grain size of L-PBF 316L is quite similar to that of conventionally manufactured 316L, and the contribution from grain boundary strengthening is estimated as 60 MPa for a grain size of 25 µm.[16]

Therefore, we suggest that dislocation strengthening must be the primary contributing factor to the high strength of L-PBF 316L, and this strengthening mechanism is closely linked to the presence of the cell structure. In terms of dislocation strengthening, the Taylor equation gives a good estimation:

$$\Delta {\sigma }_{\rho }=M\alpha bG{\rho }^{0.5}$$

expressing that the yield strength is directly related to the dislocation density \(\rho \). In this equation, M is the Taylor factor, where for a weak texture, as is typical for L-PBF 316L, the value of M can be taken as 3.06,[61] α is a factor relating to the dislocation type, typically taken to be 0.24 for FCC metals,[62] b is the Burger’s vector (0.256 nm for austenitic steel),[8] and G is the shear modulus (78 GPa). The overall dislocation density in L-PBF 316L determined using X-ray diffraction (XRD) is in the range of 1014–1015 m−2,[59,63] which is consistent with the TEM measurement of the density of paired dislocations within cell boundaries (4 × 1014 m−2) based on the cell size and misorientation angle.[16] Thus, the contribution of dislocations to the yield strength can be estimated as 146–460 MPa. This method may overestimate the dislocation strengthening because the dislocations are not uniformly distributed in the sample, but mostly are highly entangled at the cell walls.

In addition to the texture and grain morphology, the prism-like cell morphology may also contribute to the mechanical anisotropy, and therefore a more precise model for dislocation strengthening in AM alloys, taking the anisotropy into account, is needed for microstructure design and property optimization.

5 Conclusions

In this work, we have documented that the cell structure in a standard L-PBF 316L sample has a prism-like morphology in 3D. Each cell has its long axis aligned with the one of the < 001 > crystallographic directions that is closest to the local thermal gradient. In addition, we have observed 3D side-branching of cells, which happens frequently at the melt pool boundary intersections. In addition to relatively sharp cell walls, there are loose dislocation boundaries within the cell interiors, together forming a bamboo-like dislocation structure. During the L-PBF process, segregation at cell walls occurs but diminishes after a short time, thus being very weak.

The present work suggests that both the liquid–solid transformation and the thermal strain contribute to the cell formation: An initial segregation/dislocation network forms during liquid–solid transformation, and a large number of dislocations are subsequently introduced by the thermal strain, and are deposited on the initial network to form the final dislocation cell structure. By evaluating the contribution from the relevant strengthening mechanisms, it is found that the contribution from the cell structure is significant, and it is suggested that a precise model for dislocation strengthening needs to be developed.

Understanding the 3D morphology of the cell structure is crucial to explore future methods for tailoring the cell structure of L-PBF 316L, particularly by adjusting printing parameters to control the cell diameter and geometry. Additionally, insight into the formation mechanisms of cell structures allows for the control of texture and local dislocation density during the printing process, which offers promising opportunities to produce parts with optimized microstructures, e.g., with gradient or composite structures.