High levels of RS, nearing the alloy yield strength at room temperature, has been also reported in the literature5,17,35. In the present study, it could be argued that the RS values higher than the yield strength result from plastic deformation that brings the material far into the strain hardening regime, thereby increasing the actual yield limit. Since the maximum penetration depth of the SXEDD measurements for the {311} is ~ 42 µm, an assumption of a plane stress state (σnormal = 0) is considered to apply in this study. Nevertheless, a residual stress state at a level higher than the monotonic yield strength could arise from the presence of a triaxial stress state. Hence, the possibility of a triaxial state (e.g., induced by the presence of the theoretically harder micro-segregated phase present at the cell walls) cannot be dismissed and needs further investigation.

It is evident that the choice of scanning strategy has a significant effect on the magnitude and direction of RS. There is controversy in the literature about the direction along which the largest RS magnitudes are build-up. Some authors5 state that the stresses perpendicular to the scanning direction (case of scanning strategies using unidirectional vectors) are significantly larger than the stresses along the scanning direction, while others14,22 observe that the largest RS occurs parallel to the scanning vectors. In our case, the LXADD results of Fig. 2b,c indicate that the highest values occur in the Y-direction, with the two scanning strategies exhibiting similar values.

Rotational scanning strategies are generally advised for RS mitigation11,15,23,36. It is stated that rotation scanning strategies increase the uniformity of stress distribution in As-Built components. The angle of 67° is considered one of the most suitable rotation angles since the scan vector direction does not repeat (considering 10° error) for a large number of layers. However, no significant differences in the uniformity of the stress distributions of Y-scan and Rot-scan samples are observed in the plots of Fig. 2 and the stress maps of Fig. 3. Regarding the minimization of RS, it is observed that the X-direction component follows the commonly reported trend of lower magnitudes for the Rot-scan sample, the Y-direction component exhibits similar values for the two scanning strategies in the As-Built condition while the Rot-scan sample undergoes a higher relaxation after thinning, and the Z-direction component unexpectedly reverses the tendency.

The mechanism leading to the lower σZ values observed in the Y-scan sample can be explained as follows: in principle, reducing the temperature gradient (dT/dx) decreases the thermal stress developed during material processing, thereby decreasing RS. Thus, a plausible explanation could be the development of a directional thermal transfer, where the heat flux could be favored along the BD-axis during the Y-scan processing and over the SW/ SD-plane during the Rot-scan processing. This would mean that the thermal gradients are higher across the plane orthogonal to the BD-axis for the Y-scan processing, but also on the lateral surface for the Rot-scan.

Another possibility is that the reduced σZ values observed in the lateral surface of the Y-scan sample are in fact a result of its crystallographic anisotropy (i.e., columnar grains). Using Transmission Electron Microscopy (TEM), some authors have reported33,37,38 high densities of dislocations in IN718 LPBF as-built materials. These dislocations form networks that are most commonly entangled at the cell walls. Therefore, we believe that RS relaxation induced by dislocation accumulation can indeed be, at least, partially responsible for the unexpected results observed in Fig. 3.

In order to verify this dislocation accumulation hypothesis, EBSD maps were acquired at the centre of the MS1 (see Fig. 3a) to compare the amount of Geometrically Necessary Dislocations (GNDs) in the two studied samples. The EBSD data were subsequently refined using a Kikuchi pattern matching software that enables to resolve Low Angle Grain Boundaries (LAGBs) down to 0.05° (more details about this technique are given in the Materials and Methods section).

Figure 4a shows a high magnification refined Kernel Average Misorientation angle (KAM)39 map of the Y-scan sample. Grain boundary angles > 2° are displayed as red lines whereas local orientation changes < 2° are shown in black. When comparing with Fig. 1b, the LAGBs seem to correspond to subgrains formed by columnar dendrite-cells, which exhibit different degrees of misorientation (the most pronounced misorientations correspond to 1.5°). On the other hand, the subgrains observed in the Rot-scan sample (Fig. 4b) alternate mosaic and columnar dendritic-cell microstructures. KAM angle distributions (Fig. 4c,d) are used to compare the character of this misorientation. Despite the different dendritic-cell morphologies, the two materials exhibit similar distributions.

Figure 4

Kernel Average Misorientation (KAM) angle map (step size is 0.15 µm) after Kikuchi pattern matching for (a) Y-scan sample and (b) Rot-scan sample. The red lines correspond to grain boundaries with misorientations ≥ 2° and the black ones to subgrains with misorientations ≤ 2°. (c),(d) KAM-angle distributions corresponding to the EBSD maps in (a) and (b), respectively.

Unfortunately, although EBSD maps with high spatial resolution are suitable for the imaging of subgrain structures, their local nature does not enable a clear comparison between the two scanning strategies. Hence, we also performed EBSD analyses at an intermediate magnification that offers a reasonable sampling of grains, while still being able to partially resolve the subgrain structures.

Figure 5a shows an intermediate magnification EBSD orientation map acquired in the Y-scan sample. The Y-scanning strategy leads to the formation of coarse columnar grains (average width of ~ 100 µm), which lay parallel to the BD-axis, span across several layers and exhibit predominance of orientations close to {100}. Instead, the Rot-scan condition (Fig. 5b) yields smaller grains that exhibit elongated shapes. Such grains seemingly span across a lesser number of layers and seem to grow in random directions, so that no dominant crystallographic orientation is observed. The difference in the amount of KAM between the two scanning strategies is already noticeable from a qualitative standpoint (Fig. 5c,d), with the Y-scan sample exhibiting higher levels of subgrain boundaries. Note that the degree of misorientation seems to depend on the grain orientation, as some of the grains show larger populations of subgrains, especially in the Y-scan sample. The corresponding KAM distributions in Fig. 5e show a compensation between decreased population of very low-angle boundaries (< 0.5°) and increased population of low angle boundaries (0.75° to 2°) when comparing the Y-scan sample to the Rot-scan sample. An increase in the amount of high-angle boundaries with persistence of low-angle boundaries is usually related in the literature to deformation-induced microstructures39.

Figure 5

Intermediate magnification EBSD orientation maps for the (a) Y-scan sample and (b) Rot-scan sample. (c) KAM-angle maps from orientation data refined by Kikuchi pattern matching for the Y-scan sample and (d) Rot-scan sample. The red lines correspond to grain boundaries with misorientations ≥ 2° and the black ones to subgrains with misorientations ≤ 2°. (e) KAM-angle distributions corresponding to the images shown in (c) and (d).

In order to get an idea about the reproducibility of the results shown in Fig. 5, we mapped in each sample two additional, equal-sized areas under comparable conditions. Their locations are sketched in Fig. 6a, and the resulting orientation maps corresponding to the Y-scan sample are displayed in Fig. 6b,c. Interestingly, the EBSD map corresponding to the Centre-Left region (centre of this EBSD map lays at 3 mm from the free surface) exhibits a clear color change while the ESBD map of the Centre-Right region expresses a crystal orientation tendency similar to the one observed at the centre of the sample (Fig. 4a). The cumulative frequency of the KAM distributions of all six EBSD maps is shown in Fig. 6d. Irrespectively of the location, the Rot-scan sample possesses comparable KAM distributions. On the other hand, the Y-scan sample exhibits an increased inhomogeneity, where the Centre-Left region contains lower amounts of misorientation compared to the Centre and Centre-Right regions. It must be noted that the growth of large columnar grains in the Y-scan sample needs to compensate any defects during solidification by misorientations. This can result in a higher defect density and stronger misorientations. Moreover, even though the amount of grains sampled in the EBSD maps is considerable, it is still not enough to obtain statistically significant results of the studied samples. Compared to the Rot-scan sample, the increased spread of data observed in the Y-scan sample could be as well partially induced by the lower amount of grains sampled by the EBSD maps.

Figure 6

(a) Schematic illustration of the location of the MS1, with a detail showing the location of the additional EBSD maps. (b) Intermediate magnification EBSD orientation maps for the Y-scan sample corresponding to the Centre-Left region. (c) Intermediate magnification EBSD orientation maps for the Y-scan sample corresponding to the Centre-Right region. (d) KAM-angle cumulated distribution showing the results from all six EBSD maps.

Keeping in mind the aforementioned statistics limitations and the local nature of the EBSD results, we consider that Fig. 6d gives indication about the fact that the unexpected lower σZ values observed in the Y-scan sample (Fig. 3g,h) are very likely influenced by the underlaying microstructure. Large columnar grains would favor the relaxation of σZ component by an increased dislocation accumulation. The higher levels of misorientation observed in the centre and Surface 1 regions of Y-scan sample would also suggest that favorably oriented columnar grains are able to accumulate more dislocations.

Instead of proceeding with further laborious EBSD examination to increase the statistics of Fig. 6d, or even to perform High Resolution Synchrotron Diffraction (HRSD) for the measurement of dislocation structures40; the possible influence of the microstructure was re-examined on the lateral surfaces of both samples: after release from the baseplate (i.e., Released condition) we performed RS measurements using LXADD (see Fig. 7a).

Figure 7

(a) LXADD setup corresponding to the RS investigation of the Released Rot-scan sample (after baseplate removal). (b),(c) Maps of the Z-direction RS component in the Y-scan sample on Surface 2 and Surface 1, respectively. (d),(e) Maps of the RS Z-direction component in the Rot-scan sample on Surface 2 and Surface 1, respectively. The average error is ± 20 MPa.

For the two samples, the RS levels are quite similar in the bottom-half, while higher RS values are observed in the upper-half (Fig. 7b,e). However, higher RS occur in Surface 2 compared to Surface 1 for the Y-scan sample, while no significant differences are observed between the two surfaces of the Rot-scan sample. The latter finding is in good agreement with the microstructure homogeneity shown in Fig. 6d. Also, the RS state is always lower in the Y-scan sample when compared to the Rot-scan one. A possible explanation for the results of Fig. 7 would be that that the magnitude of the Z-direction RS component in the Y-scan sample is reduced by dislocation accumulation, and that this accumulation is mainly driven by larger grain sizes and favorable crystallographic orientations. The spatially dependent heterogeneity of Y-scan sample would enable the accumulation of higher amounts of dislocations in one part of the sample (adjacent to Surface 1), therefore leading to the lower RS values observed in Fig. 7c.

A considerable reduction of the Z-direction RS values is observed between the SXEDD Thin-Baseplate (Fig. 3f,g) and LXADD Released results (Fig. 7c,e). This reduction is likely induced by stress relaxation after baseplate removal (mostly occurring at the bottom), but also by the fact that LXADD and SXEDD techniques do not interrogate the same penetration depth (~ 5 µm for LXADD and ~ 42 µm for SXEDD analysis).

Our rational to correlate the bulk EBSD analysis to SXEDD measurements in the near-surface is based on the principle of RS balance, whereby the near surface regions equilibrate the bulk residual stress state. Thus, any RS relaxation occurring in the bulk material should reflect on the near-surface RS state41. It must be noted that a deeper understanding of microstructure-induced RS relaxation needs the use of monochromatic Neutron Diffraction (ND). Nevertheless, strong textured bulk microstructures such as the one observed in the Y-scan samples hampers the use of this technique (e.g., vanishing of the reflection peak for certain directions). Further work needs to be done to overcome the challenges of residual stress analysis in highly textured materials both with monochromatic and energy dispersive (time-of-flight) neutron diffraction.

The reason why it was possible to obtain linear lattice-spacing-vs-sin2(uppsi) distributions with reduced oscillations during the LXADD and SXEDD measurements (see Fig. 9c in the Material and Methods section) is because the near-surface grain structure is finer with reduced texture. As shown in Fig. 8a, the manufacturing of the up-skin layer in the Y-scan sample locally halts the epitaxial growth characteristic of the bulk material, promoting the growth of grains that span through the height of the up-skin layer. The transition between the bulk material and the up-skin layer is, however, less noticeable in the Rot-scan sample (Fig. 8b). Interestingly, the KAM distribution results of these two regions (Fig. 8e, green and black dashed lines) are shifted rightwards with respect to the bulk results. The KAM angle maps (not shown in Fig. 8 for the sake of brevity) indicate small regions of increased misorientation occurring at the border between the bulk and the up-skin; it is suggested that the processing of the up-skin layer leads to a local increase of the misorientation content in both samples.

Figure 8

EBSD orientation maps corresponding to the subsurface region below the Top Surface for (a) the Y-scan sample and (b) the Rot-scan sample; the black horizontal lines indicate the approximate location of the border between the bulk material and the up-skin layer. EBSD orientation maps corresponding to the subsurface region below Surface 1 for (c) the Y-scan sample (where white line indicates the approximate location of the transition between fine grains and larger and more textured grains) and (d) the Rot-scan sample. (e) Plot of the cumulated frequency against KAM angle, where the data that have been already introduced in Fig. 6d is shown is blue and red, and the data corresponding to the subsurface regions is shown in green and black. (f) Schematic illustration summarizing the main findings of the EBSD analysis in the Y-scan sample.

Figure 8c shows that a subsurface layer of ~ 100 µm containing finer grains is formed underneath Surface 1 of the Y-scan sample (the approximate border is shown with a white vertical line). From this depth inwards, the microstructure exhibits columnar grains, which, in general, are smaller than those observed in the bulk, and where <001>-orientation is dominant. In the case of the Rot-scan sample (Fig. 8d), and apart from a thin (~ 50 µm) layer of fine grains, the microstructure beneath Surface 1 is considered similar to that observed beneath the up-skin (Fig. 8b) and the bulk (Fig. 5b). The KAM evaluation (Fig. 8e, green and black solid lines) indicates similar results for these two regions of the Y-scan and Rot-scan samples, with the misorientation values laying between the bulk values of Rot-scan sample and the Centre-left values of the Y-scan sample.

The clarification of the KAM differences observed between the subsurface regions of Fig. 8 requires further investigation. In any case, we think that these differences are mainly driven by the processing itself and/or the local microstructure. The RS relaxation (leading to an increased misorientation content) would mainly occur in the bulk of Y-scan sample, where the conditions of large textured columnar grains are fulfilled (see Fig. 8f). Moreover, because of preferred orientation, regions with <001> dominance would be able to accumulate higher amounts of misorientation, therefore increasing the RS relaxation effect.

Overall, it is observed that an EBSD analysis of the material, even when intensively performed, might not suffice for a complete characterization of spatially dependent microstructures characteristic of AM materials, emphasizing the need for the use of complementary techniques such as texture analysis by XRD/ND and Bragg-edge tomography42.


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