Residual stress determination by neutron diffraction in powder bed fusion-built Alloy 718: Influence of process parameters and post-treatment

• Residual stresses determined using calculated and measured stress-free lattice spacings were distinctly different. • Effect of build orientation on residual stress states in EB-PBF and LPBF found to be an important determinant. • Difference in residual stresses between EB-PBF and LPBF materials established to be significant. • LPBF process parameters demonstrated to influence residual stresses in the

by additive manufacturing (AM), which is a manufacturing process that melts material layer upon layer according to a predefined design for near-net-shape part fabrication [3,4]. There are numerous benefits associated with AM such as low buy-to-fly ratio and the possibility to manufacture complex structures [3,5,6]. Nonetheless, there are some concerns with defects [7], columnar morphology [8,9], texture [10], leading to anisotropic mechanical behavior. In addition, residual stresses can be present in both laser-and electron-beam based powder bed fusion. In the laser powder bed fusion (LPBF) process, there are large thermal gradients due to the relatively cold build platform. Thus, the resulting fast cooling rates in LPBF lead to the formation of a finer microstructure and hence to an increased strength of the material. Nonetheless, in association with the higher cooling rates for LPBF, compared to the electron beam powder bed fusion (EB-PBF) process [11,12], higher residual stresses form in the material [13]. It should be mentioned that the cooling rates are typically higher in LPBF compared to EB-PBF because of the preheated base plate and use of preheating step before melting in case of the latter [13].
Residual stresses are formed from temperature variations during materials processing such as welding and AM. Additive manufacturing typically involves complex thermal cycling, and the residual stresses build up at a micro level, i.e. for each added layer, which leads to the development of macro residual stresses in finished components [13,14]. The residual stresses, particularly tensile residual stresses in the material, are undesirable, as they can deteriorate the fatigue and tensile properties [15], and make the material prone to cracking, delamination and distortion.
The process parameters used during AM have been found to influence the residual stresses in the built material [14,[16][17][18][19]. Ali et al. [17] investigated the effects of scanning strategy (scan vector lengths and scan vector rotation) and re-scanning strategy on the residual stresses in LPPF built Ti-6Al-4V and showed that 90°alternating scanning strategy resulted in the lowest residual stresses. This result was also in accordance with the findings of Robinson et al. [16] who showed that in LPBF manufactured Ti using unidirectional vectors, the residual stress was primarily oriented in the scanning direction. Mercilis et al. [18] showed that LPBF built 316L constituted of two residual stress regions, i.e., high tensile residual stresses at the top and bottom (close to the build plate), whereas in the middle, intermediate compressive stresses formed. Mercelis et al. [18] also found that the parameters that were the most important for determining the magnitude and nature (tensile or compressive) of the residual stresses were the material properties, the height of the sample, and the AM process parameters such as laser scanning strategy. Kruth et al. [14] concluded that short scan vectors and preheating of build plate are two parameters that reduce residual stresses. Moreover, it is possible to reduce the residual stresses to certain extent by optimizing the orientation of scan vectors. Another approach to reduce the residual stresses is by exposing the material to thermal post-treatments. Vilaro et al. [20] have shown relief in residual stresses in LPBF built nickel-based superalloy (Nimonic 263) after subjecting the material to annealing treatment.
Neutron diffraction [12,21,22] is a key method for characterizing type-I residual stresses which "equilibrate over macroscopic dimensions" [23,24]. Crystal lattice distortions, i.e. deviations from reference "stress-free" samples, can be measured nondestructively even in relatively thick samples due to the high penetration depth of neutrons [25]. If the lattice spacing (d) in the material is larger than the reference lattice spacing, tensile residual stresses are present, and vice-versa for compressive residual stresses. Therefore, by measuring d-spacing through neutron diffraction and comparing it to a "stress-free" lattice spacing (d 0 ), the strain (ε) in the material can be calculated. The stress-free lattice spacing is measured in reference samples which can be produced by several methods as described in [26], or can be estimated through certain assumptions and calculations [27]. By determining the stress-free lattice spacing from diffraction measurements, it is possible to eliminate the complication of disentangling the stress-free lattice spacing changes originating from compositional inhomogeneities and residual stresses, which is a common challenge for residual stress analysis in AM [27]. It should be mentioned that accurate determination of stress-free lattice spacing, d 0 , is an important concern for residual stress determination using diffraction-based techniques [26]. Notwithstanding the above, comparison of the use of different methods for d 0 determination has not been well understood. In this context it is worth mentioning other methods also exist for residual stress measurements such as, contour method, X-ray diffraction etc. However due to the destructive nature of testing in case of contour method and the limited penetration in case of X-ray diffraction, neutron diffraction for nondestructive evaluation of bulk residual stress is a promising technique [28,29]. Moreover, since the residual stresses are calculated from the strain in the lattice, the measurements are not significantly affected by the material properties, e.g., hardness and extent of cold work [11].
The objective of the study was to investigate the effect of LPBF process parameters such as, scan strategy, laser power and scan speed, on the residual stresses in the fabricated Alloy 718 material. Moreover, the influence of build orientation on residual stress was also studied. The residual stresses in the LPBF Alloy 718 were also compared with EB-PBF material. In addition, two approaches for determination of stress-free lattice spacing have been compared. The same samples tested in as-built condition, for both LPBF and EB-PBF, were also subsequently subjected to annealing treatment to evaluate the residual stress reduction. Understanding the residual stresses and how to relieve them are crucial for future applications of LPBF and EB-PBF built Alloy 718, and although similar studies have been published e.g. [12,30,31], no comprehensive study has been undertaken addressing the effect of processing parameters and post-treatments on the development of residual stresses.

Sample fabrication of LPBF and EB-PBF built Alloy 718
The LPBF built Alloy 718 samples used in the present study were provided by GKN Aerospace AB (Filton, UK). The specimens were produced using an EOS M290 machine. The nominal chemical composition of the inert gas atomized Alloy 718 powder used is given in Table 1; both the nitrogen and oxygen contents were below~300 ppm. Four sets of wall samples, each sample with dimensions 100x50x6 mm 3 , were produced with different processing parameters, and only the process parameters that were altered are stated in Table 2. Each set of samples comprised a pair of a vertical and a horizontal wall specimen as shown in Fig. 1. All the builds were fabricated using a layer thickness of 40 μm and a hatch distance of 110 μm. It should be mentioned that the sample set #1 was built using the default machine settings. After fabrication, all the samples were removed from the build plate using electric discharge machining.
One set (vertical and horizontal samples) of EB-PBF specimens was manufactured using an Arcam A2X machine, at University West, Sweden. The feedstock powder used, Sandvik Osprey® Alloy718, was manufactured using vacuum induction melting and subsequent inert gas atomization with argon gas. The resulting chemical composition is displayed in Table 1; both the nitrogen and oxygen contents were below 250 ppm. The powder was processed using the typical recommended Arcam settings [32]. The powder layer thickness used was 75 μm and the hatch distance was set to 125 μm. It should be mentioned that the powder layer thickness is the distance by which the build platform is lowered for processing of each subsequent layer. For melting, bidirectional raster strategy was used.

Neutron diffraction measurements
Neutron diffraction experiments were performed on the time-offlight POLDI diffractometer at the Swiss Spallation Source, at PSI, Switzerland. All the samples tested in as-built condition were retested after applying annealing treatment (specified later in Section 2.3). The {311} diffraction peak was used for strain evaluation because, in face centred cubic (FCC) Ni-based alloys such as Alloy 718, it is the least affected by the intragranular strain and inter-phase strains [33][34][35] and the plane-specific elastic properties are similar to those of the bulk to accurately reflect macroscopic stress in the material. For data collection, seven equally spaced points (for LPBF, whereas for EB-PBF six equally spaced points) were chosen along the width of the specimens as shown in Fig. 1. For each point, a gauge volume of 3.8 × 3.8 × 3.8 mm 3 was defined by two pairs of diaphragms perpendicular to the incident beam direction; Fig. 2 shows a schematic of the setup. This together with a radial collimator for the diffracted beam, resulted in a satisfactory trade-off between spatial resolution and counting time for this study. The gauge volume was aligned and fully submerged in the material to avoid "pseudostrains" due to partial gauge volume burial. All the points were undertaken with the center of the gauge volume being at the center of the wall thickness, i.e. at X = 3 mm. The obtained data were fitted using Mantid [36] and the fitted results were processed using in-house MATLAB scripts.

Annealing treatment and stress-free reference
The same samples that were measured in the as-built condition were annealed for 2 h at 1066°C, which is a typical homogenization treatment [37] and has been also adapted for stress relief of AM processed Alloy 718 [38]. The residual stresses in all annealed samples were measured at the same locations for direct comparison with the as-built samples. After determination of the d-spacing in the annealed samples, the sample for d 0 measurement was sectioned out as a thin strip from the vertical LPBF sample #4 (see Fig. 3 (a)). Furthermore, around the measurement points, comb-type cuts were made to further relieve the stresses in order to ensure that strain relaxes in the d 0 sample, as previously reported [33]. The reference d 0 measurement was undertaken at three points along the build direction as illustrated in Fig. 3 (a) to investigate possible variations due to microstructural or chemical heterogeneity. This has been reported to be an important aspect while measuring lattice spacing in AM manufactured material [33]. However, in the present study and within the experimental accuracy, it was seen that the variation is not so significant, i.e. in X and Z directions the standard deviation from the mean value is smaller than the experimental error, which corresponds to a strain uncertainty of only 35 με (see Fig. 3 (b)).

Neutron diffraction data analysis
For LPBF samples, the measured interplanar spacing d 0 311 was determined using an average of values evaluated from the three measurement points (bottom, middle, top) as shown in Fig. 3 (a). No significant variation in d 0 was observed at the three locations. Therefore, an average value of 1.08613 Å was used for d 0 311 measured as shown in Fig. 3 (b). Thereafter, the lattice strain was determined using the interplanar spacing, d 311 , as follows: where i = X, Y, Z represents the three orthogonal directions. Using the above residual strain measured in three orthogonal directions and the  7). The arrow indicates the build direction (BD) and the coordinate axes correspond to the strain/stress measurement coordination system. generalized Hooke's law, the residual stresses in the corresponding directions were evaluated as follows: where E is the Young's modulus and ν is the Poisson's ratio. The values of E and ν corresponding to {311} lattice planes used were 200 GPa and 0.3, after [39]. When thin walls are built [28], we can assume a plane stress state, i.e. σ XX = 0 and measuring a refence d 0 value is no longer required as previously done in [27]. Thus, d 0 can be calculated for each measurement point as follows: and the σ YY and σ ZZ can be calculated by the following equation: where i and j can be either Y or Z. An example of calculated d 0 311 is shown in Fig. 3

Electron backscattered diffraction -EBSD
Sections of the selected annealed vertical samples were extracted using alumina cutting blade, and sections along the build direction (BD) were hot mounted. All these samples were taken from a region close to the mid-height of the wall samples. The samples were then ground and polished, with a final polish using 0.05 μm silica suspension. For electron backscattered diffraction (EBSD) analysis, a field emission gun scanning electron microscope (FEG SEM) Zeiss ULTRA 55 equipped  with EDAX Hikari Camera operated at 20 kV in high current mode with 120 μm aperture was used. The EBSD raw data was post-processed using the EDAX OIM Analysis 7.3 software.

Microstructure and crystallographic texture comparison: LPBF and EB-PBF
The manufacturing processes as well as the scanning strategy greatly influence the microstructure as shown in Fig. 4 for vertical samples. EB-PBF resulted in heterogeneous microstructure with one large grain in the middle that is about 400 μm wide and longer than the field of view of the EBDS map (1.2 mm). Large elongated grains aligned with the building direction surround this grain. Whereas, the microstructure of the LPBF samples appears to be more homogeneous, and the chessboard scanning strategy resulted in the smallest grain size (Fig. 4 (b)); i.e. 25 μm (sample #4) compared to the 58 μm (sample #1) in sample produced by bi-directional raster scanning strategy. Moreover, the crystallographic texture is significantly different between these two samples. The bi-directional raster scanning strategy in LPBF sample #1 resulted in relatively mild 〈100〉 texture in BD and nearly random in X-Y plane ( Fig. 4 (a)). The chessboard scanning strategy in LPBF sample #4 caused relatively strong 〈101〉 texture along the building direction (Z) and relatively strong <100> along the in-plane direction (Y) (Fig. 4 (b)). Finally, the EB-PBF results in significantly strong <100> texture along the building direction and relatively strong near <100> texture along the in-plane directions (X and Y), mainly dominated by the very large grains in the center of the sample which reside in the middle of the neutron gauge volume (Fig. 4 (c)). The latter strong texture affects the choice of diffraction peak for residual strain calculation and it is further discussed in Section 4.2. These findings agree well with the neutron diffraction patterns obtained for all the directions measured for residual stress calculation.

As-built LPBF Alloy 718: calculated d 0 from plane stress assumption
The residual stress values from the {311} lattice planes, evaluated using the calculated d 0 (Eq. (3)), in the as-built condition for the vertical samples are given in Fig. 5, wherein the error bars represent the error propagation in determining the peak positions (by peak fitting). The evolution of residual stress σ YY , with build height followed a 'U-shaped' pattern. From the bottom of the build to the top, the nature of the stress varied from tensile to compression and then tensile again as shown in Fig. 5 (a). Comparing residual stress, σ YY , in specimen #1 and #4, which were produced with raster and chessboard strategy, respectively, revealed the latter to contain slightly lower residual stress. The nature of residual stress along the z-direction was relatively invariable for a given sample as shown in Fig. 5 (b). The residual stresses σ ZZ in the specimens #1, #3, #4 were compressive in nature whereas tensile in sample #2. The only parameter that is different between samples #2 and #3 is the laser scanning speed, which could have caused variation in cooling rate, thereby affecting development of residual stresses in the material. A study on LPBF built Alloy 718 has shown increase in scan speed to result in faster cooling rates [40]. The value of σ ZZ for specimen #4 was lower than for #1. By comparing results for samples #1 and #3 there is no observed effect of increased laser power, i.e., increase in energy input, on the residual stress. Residual stresses in the corresponding   (4); the through thickness stress (along X) is assumed to be zero. All the points were measured at the same build height. horizontal samples were much lower than in the vertical samples as shown in Fig. 6. It should be noted that the residual stresses appear compressive in both Y and Z directions, while direction X is assumed to be zero, which does not satisfy the stress equilibrium. This is due to the choice of d 0 . For the plane stress assumption, the stress in the direction X is assumed zero. The direction X corresponds to the building direction of the horizontal samples, while residual stresses are seen to be high along the building direction (refer Fig. 5 (b) and Fig. 7 (b)). As such the plane stress approximation leads to an overestimation of the value of d 0 which results in calculating (slightly) compressive stresses along both directions Y and Z. Nevertheless, if directions Y or Z are assumed as "stress-free", the calculated residual stress magnitude does not exceed ±50 MPa, which appears to be the uncertainty of the stress calculation for these samples.

Annealed LPBF Alloy 718: calculated d 0 from plane stress assumption
The stresses in all the vertical and horizontal samples (measured using {311} lattice planes) were significantly relieved after the annealing treatment and the residual stress values are shown in Fig. 7 and Fig. 8. Sample #4 was chosen because of the lowest amount of stresses in the as-built condition, to further elucidate the significant effect of annealing treatment on the residual stresses. In Fig. 7 (a) for vertical sample, after the annealing treatment the residual stress profile flattened and was close to zero. In Fig. 7 (b), the stresses in Z-direction were observed to be compressive prior to the annealing treatment, while stress relaxation was observed after the annealing treatment. These results corroborate qualitatively with the observations of lattice spacing (d), as shown in Fig. 7 (c) and (d), which does not require plane stress assumption. Fig. 8 (a) and (b) show the residual stresses (along the Y and Z-directions) and Fig. 8 (c) and (d) show corresponding lattice spacings for the horizontal samples. In this case, too, similar stress relaxation was observed after annealing treatment as the vertical samples. The (slightly) tensile stress seen in Fig. 8 after annealing is considered negligible and it arises from the measurement inaccuracy and the plane stress assumption.

Residual stresses in as-built EB-PBF Alloy 718: using calculated d 0
The residual stress values in EB-PBF obtained from the {200} lattice planes for both vertical and horizontal samples are given in Fig. 9. On average, the stresses in the horizontally built specimens were similar to horizontally built LPBF material. However, for vertically oriented samples the stresses were much lower than in the LPBF process. The application of annealing treatment on EB-PBF samples had only minor effect on the residual stresses in the material.

Discussion
As mentioned in the experimental section, all the samples were removed from the base plates and previous studies have shown that this significantly affects the residual stress state of the material [14,18]. Kruth et al. [14] showed that tensile stresses exist in the LPBF material while attached to the build plate. After removing the material from the build plate, the stresses relax which can potentially lead to shrinkage and bending of the material. It is also worth mentioning that, at high temperatures encountered during processing, the yield strength is decreased which can cause plastic deformation due to thermal stresses, which in turn results in residual stresses as elaborated by Kruth et al. [14].

LPBF built Alloy 718
The findings in this work correlate well with already published results, that LPBF built Alloy 718 is prone to significant residual stresses [31,41]. The process parameters were found to influence the residual stress state of the as-built material. The various parameters which were systematically varied are stated in Table 2. It was observed that the hatching pattern influences the residual stresses, correlating well with the literature [16,18]. Lower amount of stress was observed for the vertical sample produced using chessboard strategy compared to the bi-directional raster scanning strategy (see Fig. 5), which has also been previously reported elsewhere [42]. The chessboard scan strategy is composed of squares of vectors, where neighboring squares have vectors aligned 67°with respect to each other. As it has been shown that the vectors are aligned with the residual stresses [16], it is possible that there is a superposition of the micro residual stresses, leading to a decreased macro residual stress level. The lower amount of residual stresses observed for chessboard strategy compared to raster strategy can also be explained by the more homogenous heating of the powder-bed in case of the former strategy, which would have reduced the thermal gradients thereby lowering the thermal residual stresses [43]. To gain further understanding of the effect of processing conditions, simulations can be performed, and the data from the present study can be used for calibrating such simulation models.
The magnitude of the residual stresses in the as-built material was dependent on the build orientation and height from the built plate. As shown in Fig. 5 (a), the residual stresses were tensile close to the build plate (point 1) and at the top (point 7) of the specimen, whereas they were compressive in the middle of the material. This too corresponds well with the findings of Mercelis et al. [18] as they had also similarly tested the samples after removal from the build plate. Kruth et al. [14] have explained this occurrence to be due to removal of the sample from the build plate, which changes the stress state in the material. There is a difference in the two graphs in Fig. 5 (a) and (b), in the Z direction the residual stresses are somewhat constant in nature-tensile or compressive (depending on the process parameters), while in Y direction they change from tensile to compressive to tensile. On the other hand, in horizontal sample, for stresses in Y direction, (Fig. 6 (a)), no U-shape (tensile-compressive-tensile) in the residual stress profile was observed, while in Z direction (Fig. 6 (b)) the trend is similar to in Fig. 5 (b), i.e., relatively constant stress level, though close to zero. The reason for this difference in vertical and horizontal sample (Y direction stresses) can be explained by the difference in the build orientation of the two investigated samples. For the horizontally built sample, the material is in contact with the build plate throughout the whole building time, corresponding to only the bottom point for the vertically built material, therefore this U-shape and stress variation linked to build plate offset cannot be observed. These stress variations could still be present throughout the thickness. However, due to limitations of the POLDI instrument, these could not be measured. Mercelis et al. [18] have also observed reduction in residual stress for lower build heights. It should be noted that the residual stresses do not appear to equilibrate, i.e. they do not seem to cancel each other as they all appear to be compressive. This is a result of the assumption that the stress is zero in the direction parallel to the wall thickness, which for this sample is parallel to the building direction along which typically the highest residual stresses are seen (see Fig. 5 (b)).
It was observed that the chessboard scanning strategy results in lower amount of residual stresses compared to the bi-directional raster scanning strategy. Further annealing treatment significantly reduced the residual stresses as shown in Fig. 7 and Fig. 8. The result of the annealing treatments corroborate well with Kruth et al.'s [14] observation for Ti-6Al-4V produced by LPBF.

EB-PBF compared with LPBF
Due to the strong crystallographic texture in EB-PBF samples, residual stresses were calculated using the {200} lattice planes, the results are shown in Fig. 9. When strongly textured materials are measured, the strong texture affects the intergranular microstrains accumulated during plastic deformation, which result in spurious residual lattice strains [44,45]. This makes the choice of diffraction peak particularly crucial for the correct characterization of residual strains. However, it was observed that the lattice strain variation along the 3 directions for the EB-PBF is negligible, thus negligible residual strains exist, and    1) and (2)). The arrow indicates the build direction.  1) and (2)). All the points were measured at the same build height.  1) and (2)). The arrow indicates the build direction.
investigations on stainless steel (SS316L) manufactured by AM, where the stress values evaluated using neutron diffraction on {311} and {200} lattice planes were found to be in good agreement [28]. The results showing lower amount of residual stresses observed in EB-PBF samples compared to those by LPBF corroborate well with the previous work by Sochalski-Kolbus et al. [13]. The lower residual stress in EB-PBF sample can be explained by two factors: high powder-bed temperature and application of preheat step prior to melting. The applied high powder-bed temperature during EB-PBF process (~1000°C) reduces the thermal gradient between the build plate and the layer being processed. Since residual stresses arise from temperature gradients, such processing conditions contribute to the reduction of residual stresses during EB-PBF, which is not the case during LPBF processing where steeper temperature gradients are expected [47].

Influence of d 0 on evaluation of residual stress in LPBF Alloy 718
One of the greatest concerns when determining residual stresses using diffraction-based measurements is the stress-free lattice spacing, d 0 [26]. Therefore, in the present study, d 0 was evaluated in two ways: (a) calculated d 0 by plane stress approximation, (b) measured d 0 using 'stress-free' reference sample. The results using the former approach are already discussed in Section 4.1, and those from the latter are given in Fig. 10 to Fig. 13, which were obtained using the 'stress-free' sample extracted from the annealed specimen shown in Fig. 3 (a). As shown in Fig. 11, all stress components for the as-built LPBF horizontal samples were compressive, which is not plausible in reality and, therefore, it can be inferred that this approach might be inaccurate and it implies that neither annealing nor the comb-type sectioning completely relieved the residual stresses. Moreover, the annealing treatment, prior to d 0 determination, was likely to have altered the chemical composition and consequently the d 0 value [48]. Since the annealing treatment was applied at 1066°C for 2 h, it is expected to have led to significant, if not complete, dissolution of all the secondary phases, except carbides [49,50]. In addition, the application of quenching (1066 to 500°C in~5 min) after the hold time would have inhibited any considerable precipitation [51]. Therefore, the use of d 0 evaluated using plane stress approximation appears to be more appropriate in the present case because it gives reasonable results which corroborate with the existing literature, whereas those evaluated using the measured d 0 approach appears to overestimate the magnitude of residual stresses (see Fig. 5 vs. Fig. 10 and Fig. 6 vs. Fig. 11) while the annealed samples appear to contain residual stress (see Fig. 7 vs. Fig. 12 and Fig. 8 vs. Fig. 13), which is unexpected. Adopting the calculated d 0 approach also removes the need for stress-free references and accounts for the spatial variation in chemistry and microstructure. This accounts for any effect of compositional inhomogeneity on d-spacing and its consequent effects on calculated strains and thus stresses. Withers et al. [26] predict that local compositional changes in the alloy can have much larger influence on the lattice parameters in comparison to residual stress. It is noteworthy that, Rangaswamy et al. [28] studied a 5 mm thick stainless steel (SS316L) wall manufactured by AM and found through thickness stress, measured using neutron diffraction, to be negligible.

Conclusion
In this work, the residual stresses in Alloy 718 built using two powder bed fusion additive manufacturing processes, i.e., electron beam powder bed fusion (EB-PBF) and laser powder bed fusion (LPBF), have been analyzed. Both the influence of process parameters and thermal post-treatment on the residual stresses have been investigated using neutron diffraction. Neutron diffraction was found to be a convenient tool for measuring the residual stresses of additively manufactured materials, especially for non-destructive evaluation. Based on the experimental work the following conclusions could be drawn: Fig. 13. Residual stress along (a) X, (b) Y and (c) Z directions in the horizontal LPBF sample #4 before (AB) and after heat treatment, using measured d 0 (Eqs. (1) and (2)). All the points were measured at the same build height.
• In as-built condition, chessboard scanning pattern compared to bidirectional raster scanning resulted in lower amount of residual stresses in the material. • Vertically built material showed presence of a tensile-compressiontensile stress gradient in the material, whereas stresses in horizontally built material were relatively constant and lower in amount. • Heat treatments at 1066°C for 2 h greatly reduced the residual stresses in the material. • Significantly lower residual stresses were found in as-built EB-PBF material, compared to the LPBF, which is attributed to the lower temperature gradient in the former. • The measured d 0 was significantly influenced by how the stress-free reference sample was produced, i.e. how the comb-type cuts relax stress or if annealing introduces chemical variations. • Unlike measured d 0 , calculated d 0 assumes a plane stress condition, gives reasonable results for thin-walled samples, however, it might not be valid for thick material.

Data availability
The raw/processed data required to reproduce these findings cannot be shared at this time due to technical or time limitations.

Declaration of Competing Interest
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.