Characterization of surface asperities to understand its effect on fatigue life of electron beam powder bed fusion manufactured Ti-6Al-4 V

Surface asperities play a leading role in determining the fatigue life of as-built Ti-6Al-4 V components manufactured by electron beam powder bed fusion (PBF-EB). Several roughness parameters are available to characterize the surface asperities This study focuses on identifying the surface roughness parameter that correlates best with fatigue life. To this end, several fatigue test specimens were manufactured using the PBF-EB process and utilizing different contour melting strategies, thus producing as-built surfaces with varying roughness. The focus variation microscopy technique was employed to obtain surface roughness parameters for the as-built surfaces. Selected specimens were characterized using x-ray computed tomography (XCT). Tomography can detect surface-connected features obscured by other parts of the surface that are not visible through optical microscopy. The fatigue life of all specimens was determined using four-point bend testing. Through regression model analysis, maximum pit height (Sv) was identified as the statistically significant roughness parameter with the best fit affecting fatigue life. The fracture zone was closely inspected based on the data collected through XCT prior to fatigue tests. This led to another estimate of the worst-case value for the statistically significant roughness parameter S v . The S v parameter values obtained from optical microscopy and XCT were used as the initial crack size in a crack growth model to predict fatigue life. It is observed that life estimates based solely on optical measurements of S v can be overly optimistic, a situation that must be avoided in predictive design calculations.


Introduction
In recent years, metal additive manufacturing (AM) has gained more popularity because of its ability to manufacture complex geometries to its near-net shape.However, the surface asperities, which can be detrimental to the fatigue properties, make it challenging to utilize the AM components in their as-built surface condition for fatigue-critical applications [1].In such applications, secondary production processes such as machining have been employed to achieve the final surface requirement, which however increases the manufacturing cost [2].Furthermore, the amount of material removed to achieve the final part geometry depends on the as-built surface asperities generated by the AM process.Among the different AM processes, parts manufactured by electron beam powder bed fusion (PBF-EB) have been reported to have larger surface asperities, which negatively impact the mean fatigue life [3].The large surface asperities in PBF-EB were primarily attributed to the use of coarser powder particles and higher layer thickness in the build [4].In addition to layer thickness, different contour melting strategies contribute to the surface roughness of the PBF-EB as-built part [5].
Ti-6Al-4 V is one of the most popular α + β titanium alloys for manufacturing using the PBF-EB process.PBF-EB manufactured Ti-6Al-4 V has an enormous potential to be used by the aerospace industry primarily because the as-built static properties are comparable to the conventional counterparts [6].However, the surface roughness and near-surface defects in the as-buit condition could be detrimental to parts used in fatigue-critical applications.Post-process heat treatment, such as hot isostatic pressing (HIP), may effectively close the defects in the bulk material.In contrast, the surface-connected pores and valleys remain unaffected by the HIP treatment [7,8].Post-process material removal techniques such as machining or chemical milling are generally employed to remove the surface features affecting the fatigue life.
However, any such additional post-processing activities increase the production time and cost of the component.Therefore, it is vital to understand the effect of various input factors on surface roughness to maintain the quantity of defects at acceptable levels in as-built parts.The surface quality of PBF-EB manufactured Ti-6Al-4 V could be influenced by powder size [9], build geometry [10] and process parameters [11].Among the process parameters, there are several factors, such as layer thickness, beam speed and current, and the different contour themes that influence the final surface quality [5,12].The current work mainly focuses on the effect of different contour themes on surface properties and in turn fatigue life.
Parts manufactured by PBF-EB typically have two inner contours and one outer contour.For such standard contour themes, the depth of the innermost contour to the surface ranges between 800---900 μm, depending on the effect of spot size and heat-affected zone [5,13].In the present study, as-built surfaces were manufactured by varying the number and order of the contours to investigate their effect on surface quality.Several parameters exist to quantify the surface roughness per ISO 25178-2 [14].Arithmetical mean height (S a /R a ) is the most widely reported measure in the literature to quantify surface roughness.However, to understand the impact of surface roughness on fatigue life in PBF-EB manufactured Ti-6Al-4 V, other areal height parameters such as maximum pit height (S v ), maximum height (S z ), skewness (S sk ), kurtosis (S ku ) have been reported [13,15,16].The current work is a comparative study involving all these surface parameters to determine the statistically significant parameters for fatigue life.Other researchers have previously identified Sv as the most statistically significant parameter for fatigue life of PBF-L Inconel 718 [17] and PBF-EB Ti-6Al-4 V [18,19].
For topography characterization of as-built surface asperities, different techniques such as profilometry, white light interferometry, focus variation microscopy (FVM), and confocal microscopy are typically used [20].One of the limitations with these traditional techniques is that the surface-connected features hidden beneath the as-built surface cannot be characterized [21].The worst-case surface-connected defect that initiates a fatigue failure could be potentially concealed beneath the surface by the partially melted powder particles [17].X-ray computed tomography (XCT), on the other hand, could be a complementary technique to detect and characterize such hidden surface features [17,21].The present work extracts the topography information from XCT reconstructed data as height maps.Other researchers have previously found in PBF-L Inconel 718 [17] and PBF-EB Ti-6Al-4 V [18,19] that the Sv obtained from line-of-sight surface roughness measurement techniques were less accurate than Sv obtained from XCT because the surface features often obscure other surface features.Further, the S v values obtained from XCT have been used to evaluate its impact on the bend fatigue life of PBF-L alloy 718 [22].The current work investigates the effect of S v obtained through XCT on the four-point bend fatigue life of PBF-EB Ti-6Al-4 V.
To predict fatigue life from a known initial crack size derived from as-built surface roughness in metal AM components, researchers have used either linear elastic fracture mechanics (LEFM) models [7,23,24] or Kitagawa-Takahashi diagram [18,25].Researchers have utilized either directly the surface roughness parameter (R v or S v ) [23] or ̅̅̅̅̅ ̅ 10 √ times the surface roughness parameter [26] as the initial crack size to predict fatigue life.In the present work, S v obtained directly from microscopy and XCT techniques were considered as the initial surface flaw size in LEFM life predictions.Persenot et.al [18], in their work on fatigue performance of thin struts, made use of S v to identify the "killer" defectthe defect that eventually leads to fatigue failure.Subsequently, they used the √(area) of the killer defect as the initial crack size (following Murakami [27,28]) in conjunction with the Kitagawa-Takahashi diagram to calculate the fatigue limit of test specimens under tensile loading.In the present work, S v obtained directly from microscopy and XCT techniques were considered as the depth of an initial surface flaw size in LEFM-based life predictions.The determined initial crack size is used along with the crack growth properties of the material to calculate the fatigue life under bending load.Note that while the approach using the Kitagawa-Takahashi diagram is strictly connected to the fatigue limit of the material, the focus in the current work is calculation of finite fatigue life under given stress cycle.These calculation results are compared with the life obtained from fatigue testing of four-point bend specimens.

Material and methods
The material investigated in this study was manufactured with an ARCAM Q20 plus machine using plasma-atomized Ti-6Al-4 V powder as a feedstock.The powder has a particle size distribution of 45-105 μm with a mean diameter of 69 μm.The standard process theme of 5.2.24 was modified to adopt different contouring strategies in the build.For the specimens considered in the current work, the melting order (hatch last or hatch first) and the number of inner contours (3 or 2) have been varied.Fig. 1 shows the different build themes investigated, with the standard contour (SC) shown at the middle.Other variations include contour overlapping hatch (CO), extra contour (EC), contour last (CL), and contour last preceded by trick heat (CL+TH).A detailed description of the contour melt themes, and trick heat are provided in a previous research work [29].Rectangular bars with a cross-section 20 mm x 5 mm were built to a height of 360 mm, out of which the 60--110 mm length portion were used for as-built surface evaluation as shown in Fig. 1.The details of the four-point bend test specimen in Fig. 1are provided in section 2.3.The top view in Fig. 1 shows the arrangement of samples in build layout (one sample for each of the five contour themes repeated four times), so there were 20 samples.

As-built topography characterization using microscopy
The topography of the as-built surface was investigated by focus variation microscopy technique using an Olympus DSX1000 digital microscope.Each four-point bend specimen with as-built surface condition was characterized at 10 different locations, and each measurement covered an area of 1 x 1 mm.The extracted surface from the measurement was evaluated as per ISO 25178-2 [14].The surface was first subjected to tilt correction that fits a nominal form.Later, a L-filter with a nesting index of 800 μm is applied to remove the waviness.The inbuilt software in the DSX microscope was used to analyse the roughness profile and obtain the various areal surface roughness height parameters.

XCT analysis
One four-point bend specimen with an as-built surface from each of the five contour themes was investigated using a Waygate v|tome|x M 240 XCT system.The microfocus X-ray tube was operated at 145 kV with the current adjusted to yield an X-ray focus spot size of around 8.3 μm.The data was reconstructed (voxel size 8.3 μm) with Waygate Datos|x using its built-in Feldkamp-Davis-Kress algorithm.A 3x3x3 voxel median filter was applied to the reconstructed data, and further postprocessing was performed in the software Dragonfly 2022.2 [30].An in-house procedure to quantify the height and depth of the peaks and valleys was derived and implemented in Python to interact with Dragonfly.The peaks and valleys were quantified as 2D height maps where the intensity represents the height and depth of the peaks and valleys of the scanned as-built surface.The procedure for extracting the height map from the XCT data is shown in Fig. 2, and an overview of the steps involved is described in the following section.
Step − I a) shows the side view of the four-point bend specimen as one XCT 2D slice.The 30 mm measured surface corresponds to the total length of the as-built surface.Step − I b) shows the section view of one slice where a 12.5 mm measurement corresponds to the width of the asbuilt surface.The blue box in step − I b) shows a cropped volume region closer to the as-built surface, as the current work primarily focuses on surface characterization.In step − II a) to segment and extract the asbuilt surface, thresholding is first applied using lower Otsu [31] with additional refinement.By refining the thresholding intensity, the segmentation is subjectively approximated to be within a few voxels from the ground truth.Other more optimal thresholding methods might be suitable but have not been explored as it was not the focus of this work.After thresholding, the region outside the bulk material covering the entire surface (30 mm x 12 mm) is generated as a surface-connected region (3D region with 6-connectivity).In step − II b), the peaks and lowest valleys were identified from the surface-connected region by iterating over the voxel x-coordinate and assigning the maximum voxel y-coordinate (within the region) as the peak or valley voxel.The average y-coordinate of the assigned maximum peak/valley voxels was used to determine the mean line in step − III.In step -IV a) the distance (in number of voxels) of the peaks and valleys to the mean line was  The surface height maps extracted through XCT were analysed in Gwyddion 2.65 [32].The surface height maps were subjected to standard tilt correction and a high pass filter (L-filter) per ISO 25178-2 [14] to remove the waviness and determine the areal roughness parameter S v .The S v parameter analysed in the region between the loading rollers in Fig. 3 represents the global S v .Additionally, one-half of the fractured specimen has been scanned and overlaid on top of the initial scan data.As shown in Fig. 3, the fracture did not occur in one plane, so the region around the fracture has been identified and cropped from the height map to obtain the local S v parameter in the fracture region.
The long chain of data processing operations from the raw XCT reconstruction data to the S v value, all with their uncertainties, makes it difficult to derive the uncertainty in S v with high confidence.However, with the data type and analysis in this context, the uncertainty in S v can be approximated to be at least the voxel size.

Four-point bend fatigue test
For fatigue investigations, samples built at a height between 60--110 mm were prepared with 30 mm x 12.5 mm as-built surface area and machined to a thickness of 4.75 mm, as shown in Fig. 1.An Instron 8802 servo-hydraulic machine was used for testing at a load ratio of R=0.1 and a frequency of 5 Hz.The cyclic load is applied through the top rollers spaced 20 mm apart, as shown in Fig. 3.The loading was such that the maximum bending stress on the specimen outer surface varied between 59.1 MPa and 591 MPa by using a sinusoidal wave form and the variation in recorded peak load was less than 1 % of the intended value.Since the primary interest was to evaluate the effect of contour themes on fatigue life, all tests were performed at one stress level for ease of comparison.

Statistical analysis
The effect of different topography parameters on fatigue life has been evaluated by a regression model using the "curve fitting toolbox" in MATLAB [33].As will be described in the next section, the roughness parameters have been used as initial crack size in fracture mechanics based life predictions.Thus, for consistency, the power function in the regression model has been used to relate the roughness parameters with fatigue life.The goodness of fit for the regression model has been determined by the coefficient of determination (R 2 ).A higher R-squared value generally represents a higher percentage prediction of the dependent variable from the independent variables or, in other words, a good fit of the data.The statistical significance of the regression model for the respective roughness parameter has been evaluated by checking the probability value (p-value) on the F statistic hypothesis test.The roughness parameter that results in a p-value < 0.05 has a statistically significant effect on fatigue life.The "fitlm" function in MATLAB was used to perform F-test for individual regression models.The Pareto effect analysis was performed in Minitab, LLC (2021) [34] to visualize the roughness parameters that have a statistically significant effect on fatigue life.

Fatigue crack growth model for life calculation
Fatigue life predictions based on the measured roughness parameters from microscopy and XCT were made using the commercial software NASGRO v10.1 [35].From the standard library of 2D crack cases available in NASGRO, "SC30, "semi-elliptical surface crack in plate" has been chosen for life predictions of specimens with as-built surfaces.The rectangular cross-section of the test specimens, combined with the fact that the fatigue cracks initiate from the surfaces of the specimens (as revealed by fractography), make this crack model (SC30) the most appropriate choice.The significant roughness parameter measured using microscopy and XCT was used as the initial defect size in the depth direction.The surface length of the initial crack was taken as twice the depth.Such a choice for the surface length is employed to compensate for the fact that only one initial crack represents several neighbouring valleys.Near the fracture region, the local roughness parameter was evaluated using the XCT data.The fatigue crack growth in the Paris region is given by where the stress intensity factor range, ΔK = YΔσ ̅̅̅̅̅ ̅ πa √ , in which Y is geometric correction factor, Δσ is stress range, , a is initial crack size, C and m are material constants.The da/dN vs. ΔK values for the Paris region from the previous work [36] have been adjusted using a walker correction [37] as described by Two different values of the Walker parameter (n = 0.9 for R<0 and n = 0.5 for R>0) were used in Eq. ( 2) for correcting the R-ratio from R=-1 to R=0.1.The resulting da/dN curve is plotted in Fig. 4 and matches well with previously published data in literature [38].

Metallographic investigation
For microstructure investigation, the grinding and polishing of the samples were performed following standard material characterization procedures for titanium alloys.The polished samples were etched by applying Barker's reagent (84 ml H2O+16 ml 50 % HBF4) with a cotton swab for about 10-12 s.For α lath thickness measurement, images were acquired at high magnification using a light optical microscope (LOM) Zeiss AL10.The measurement of α lath thickness was performed following the method suggested by Ridley [40] for interlamellar spacing measurement.

Fractography
ZEISS GeminiSEM 450 scanning electron microscope has been used to investigate the fracture surfaces of samples from the four-point bend test.Fractography was performed at two different magnifications.Low magnification was used to identify the different zones in the fracture surface.On the other hand, high magnification was utilized to investigate the crack initiation site and defects in the near-surface region in detail.

Surface characterization using FVM
The box plot representing the variation of different areal roughness height parameters for each contour theme is shown in Fig. 5 a) to e).
Each of the roughness parameters has 40 measurement values for each contour theme and a wide scatter is observed within the same contour theme (represented by the shape of the box plot) for all the roughness parameters.Results from ANOVA shown in Fig. 5 a) to e) have a p-value < 0.05 for all the surface roughness parameters, indicating that at least one of the contour themes has a statistically significant difference in the roughness mean values.Moreover, observing the mean roughness values in Fig. 5 a) to c) indicates a possible trend in the variation of mean values for the various contour themes.Further, multiple comparisons of mean values of the roughness parameters in Fig. 6 indicate that samples with CL+TH contour themes have statistically significant different means as compared to samples built with contour first themes (CO, EC and SC).In the case of S a parameter, samples built with the CL theme have a statistically significant different roughness mean as compared to contour first themes.Meanwhile, for the S v and S z parameters the samples manufactured with the CL theme show a trend of increase in roughness values even though there is no statistically significant difference in the mean compared to all the contour first themes.

Microstructure
The microstructure for the contour themes (SC and CL+TH themes) that have statistically significant differences in surface roughness and with the same number of contours are shown in Fig. 7.The images were taken in a plane perpendicular to the build direction.As shown in Fig. 7, the α laths are qualitatively similar for both contour themes.The average α lath thickness is 1.54 ± 0.31 and 1.43 ± 0.23 µm for the SC and CL+TH contour themes, respectively.

Regression and Pareto effect analysis
Fig. 8 a-e shows the regression plots with the R-squared and p-value for the different roughness parameters versus fatigue life.The relationship between roughness parameters (S v , S a , & S z ) and fatigue life follow the power function, therefore, the regression plots shown in Fig. 8 a-c are plotted on a log-log scale.Even though all the analysed Fig. 4. Crack growth versus ΔK at R=0.1(green circles) derived using Walker correction from experimental data obtained at R=-1 [36].Fatigue crack growth data from the literature for PBF-EB manufactured Ti-6Al-4 V tested at R=0 [39] and R=0.1 [38] are shown for reference.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)roughness parameters resulted in a low R-squared value, few parameters have p-value < 0.05.Parameters S v , S a , and S z have been reported to have a combination of low R-squared and a low p-value, indicating a low goodness of fit with a statistically significant trend in the relation between the dependent and independent variables.On the other hand, parameters S sk and S ku with a low R-squared and a high p-value indicate a low goodness of fit with no statistical significance.The statistically significant parameters show a clear trend of decreased fatigue life with increased roughness.To better visualize the statistical significance, the Pareto effect analysis is shown in Fig. 8 f.The threshold value corresponding to the statistical significance at a 95 % confidence interval for the different individual regression analysis is 2.10.The parameters exceeding this threshold value are statistically significant.

Fractography
The fracture surfaces of the specimens investigated in as-built conditions are shown in Fig. 9.In all the specimens, crack initiation   , c) arithmetical mean height (S a ).The CL+TH contour theme (highlighted in red) has a statistically significant difference in means as compared to the contour first themes (CO, EC and SC) (highlighted in blue).The CL theme ((highlighted in grey) for S a also has a statistically significant difference in mean value compared to the contour first themes.In the case of Sv and S z , even though the CL theme (highlighted in grey) does not have a statistically significant different mean compared to all the contour first themes, it still shows a trend of increasing roughness value.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)occurred at multiple locations originating from as-built surface asperities (primarily valleys) that grow and merge into raised ridges, as shown by white arrows in Fig. 9 a.The fracture surfaces are further divided into crack propagation and final fracture regions, indicated by white dots in Fig. 9.A series of lack of fusion (LoF) defects were observed in the hatchcontour interface, highlighted by green markings in Fig. 9 b.The white dashed rectangle in Fig. 9 a-c indicates the region with sharp surface asperities and near-surface defects that are shown at a higher magnification in Fig. 9 a.1-c.1.Features such as sharp valleys observed in the asbuilt surface highlighted by the blue circle in Fig. 9c.1 did not act as the primary crack initiation site.Near-surface defects such as pores highlighted by the brown circle in Fig. 9 a.1, and LoF defect in the hatchcontour interface region highlighted by the green circle in Fig. 9b.1, also did not initiate the fatigue failure.

XCT analysis
The results from the characterization of the region under stress in the four-point bend specimen (global region) and fractured region (local region) for each contour theme are shown in Fig. 10.The grayscale height map represents the height of peaks and valleys in the global and local regions obtained from post-processed XCT data.The false colour

Fatigue life estimation
The results from the fatigue life predictions, using the S v parameters obtained from different techniques and regions as the initial defect size in NASGRO, are shown in Table 1 and in Fig. 11.Additionally, the FVM-S v predictions for specimens that did not undergo XCT scanning were plotted in Fig. 11.The parameters used to model the crack in the SC30 crack case have been provided as a inset in Fig. 11.The defect sizes obtained from various techniques used for life estimation are listed in Table 1.A ratio of actual life (from fatigue test) to predicted life (from fracture mechanics calculation) equal to one (A/P=1) indicates a good estimation of fatigue life, represented by the parity line in Fig. 11.
Predictions with A/P>1 (below parity line) are conservative, while for A/P<1 (above parity line) the predictions are non-conservative.The A/ P ratio for most FVM-S v predictions is above the parity line.The FVM-S v * prediction band ranges between 0.76 > A/P>0.52, which is highlighted by a region in blue.The * sign indicates FVM based S v measurements on specimens that were characterized with XCT.In contrast, the predictions using local and global XCT data are distributed on either side of the parity line (1.39 > A/P>0.77), and the range is highlighted by a region in green.The lines corresponding to A/P=0.5 and A/P=2 are shown for reference.

Discussion
The wide scatter in the roughness measurements for the same contour theme in Fig. 5 indicates that there could be more variables other than contour themes affecting the surface quality.However, close observation of the mean values for the measurements, particularly the S v , S z , and S a parameters in Fig. 5, indicates that melting the contour last may negatively affect these surface roughness parameters.Further, Fig. 9. Fractography of specimens investigated with as-built surfaces.Profiles marked in white dots differentiate the crack propagation region from the final fracture.a) and a.1) Multiple crack initiation from as-built surface grows and merges, forming raised ridges.White arrows represent crack growth direction.The near-surface defect (brown circle) did not initiate failure.b) and b.1) lack-of-fusion defects (green markings) in the hatch-contour interface did not initiate failure.c) and c.1) Multiple crack initiations even in the presence of a sharp surface valley feature (blue circle).(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)comparing the mean roughness values in Fig. 6 indicates a trend of higher roughness values for the contour last themes than the contour first themes, with the CL+TH theme having a statistically significant different mean roughness value.Ethan et al. [41] reported that performing the contours after hatching with non-multispot melting typically produced a smoother surface in PBF-EB.The possible reason for observing the opposite effect in current work could be that the multispot contour melting performed with a low current did not have sufficient energy to remelt the asperities formed along the edges of the hatch.
In Fig. 5 the difference in surface roughness parameters (S v , S z , and S a ) between 3 contours (SC) and 4 contours (CO and EC) could not be clearly visualized due to the scatter in the roughness data.Moreover, the mean roughness values in Fig. 6 do not show any statistically significant difference for the CO, EC and SC contour themes.Therefore, adding one extra contour may not be sufficient to observe any substantial effect of the number of contours on surface roughness.Mallipeddi et al. [5] did not observe a significant improvement in surface quality when increasing the number of contours from 3 to 5 [40].Further, as shown in Since the variation in fatigue life had a smaller spread, it was challenging to visualize a significant effect of surface roughness on fatigue life.Still, the specimen manufactured with contour last theme, which had relatively rougher surfaces, resulted in lower fatigue life.Investigation of the fracture surfaces, as shown in Fig. 9, revealed that multiple cracks initiated as neighbouring locations were growing and merging into ridges in all specimens investigated with as-built surfaces.Sandell et al. [42] also reported similar multiple crack initiations in the as-built surfaces of PBF-EB manufactured Ti-6Al-4 V.Under these conditions, the crack propagation phase dominated the fatigue life as the initiations would have occurred during the early fatigue cycles [13].Surface asperities with more valleys than peaks reduce the effective load-bearing cross-sectional area, further accelerating the failure rate [13].The presence of other near-surface defects did not act as the only initiation sites for failure.A series of LoF defects was observed near the hatchcontour interface, predominantly for specimens built with contour last themes, as shown in Fig. 9b.The location of these LoF defects corresponds to the band where each hatch pass turns.Towards the end of each hatch pass, the speed is increased without increasing the beam power to reduce the heat accumulation, resulting in reduced energy density, which leads to the accumulation of LoF defects in the hatch-contour interface [13,43].The low-energy contours performed after hatching may not effectively melt these LoF defects in contour last themes, making LoF defects more evident in contour last themes.Even though these LoF defects did not initiate the failure, they may potentially reduce the effective cross-sectional area, and thereby contributing to a lower fatigue life.It has also been reported that defects such as deep sharp features, as shown in Fig. 9c, did not act as a single initiation site for fatigue failure [42].
Among several areal surface roughness parameters, the height parameters are considered to be the most relevant for investigating the effect of surface quality on fatigue life [13,15,16].Fig. 8 shows the effect of these different height parameters on fatigue life through regression models.All the analysed height parameters resulted in a low R 2 value, indicating poor goodness of fit.However, few parameters had a low Pvalue, indicating that those roughness parameters are statistically significant.As shown in Fig. 5, the average S sk values for all the contour themes were negative, indicating more valleys than peaks in the measured surface.Also, in Fig. 5, the S ku measurement for all the contour themes was > 3, indicating a spikiness in the valleys which may act as stress raisers.However, the effect analysis in Fig. 8 f shows that these roughness parameters do not have any statistical significance on fatigue life.The P-value in Fig. 8 indicates that S v , S z, and S a are statistically significant.Further, the effect Pareto chart in Fig. 8 f clearly shows that the S v is more statistically significant.Kahlin et al. [44] also chose S v instead of S a as the most suitable surface roughness parameter to establish the fatigue limit for PBF-EB manufactured Ti-6Al-4 V.
Analysing the XCT data revealed surface-connected defects hidden beneath the surface, which could be detrimental to fatigue life.Plessis et al. [21] also evaluated the role of XCT in revealing the fatigue-critical hidden surface-connected deep notches that were not captured by traditional roughness characterization techniques.The S v measurement using the XCT data in Fig. 10 shows that the S v values in the global region for the different contour themes were about 2x times higher than the average S v from FVM shown in Fig. 10.The primary reason for XCT based measurements resulting in higher S v values is because XCT data includes surface-connected hidden valleys for calculating S v, as shown in Fig. 2 (Step IV), facilitating an improved characterization of surface valleys.Further, a larger area (20 mm x 12 mm) has been evaluated in XCT, whereas the FVM measures 1 mm x 1 mm at 10 locations, which also contributes to the difference in S v .However, analysing the fractured specimens indicated that fracture did not occur in the location of the maximum valley depth in the global region for most of the specimens.Therefore, the S v measurements were performed on the local fracture region, as shown in Fig. 10.The local XCT S v values were not significantly different from the global S v values, indicating several valleys in the as-built region with depths comparable to the local S v initiating the failure, which could be one of the reasons for having multiple crack

Table 1
Summary of fatigue life estimation based on FVM and XCT S v measurement for one specimen from each contour theme.The * sign indicates the FVM based S v measurement of the specimens for which XCT was performed.
initiations starting from the valleys, as shown in Fig. 9.
Defining the initial crack size is crucial to predict fatigue life appropriately using fatigue life estimation models.In the case of powder bed fusion manufactured materials, it has been proposed that it would be appropriate to use the maximum valley depths as initial crack size for life predictions [24,45].Therefore, the fatigue life estimations were performed using the S v measurements from FVM and XCT in the current work.Fig. 11 reveals that the life estimation using the FVM data results in a non-conservative life prediction.Since the A/P ratio for all the FVMbased S v was above the parity line (A/P=1) in Fig. 11, it indicates that the predicted life was always higher than the experimental life, resulting in non-conservative predictions.However, when using XCT-based S v (global and local) for life estimation, the A/P ratio ranged between 0.77 and 1.39.The deviation from the parity line occurred in both directions, which means the predictions were either 39 % lower than actual life or 23 % higher than actual life.The deviations observed in the A/P ratio using XCT-based S v are less substantial, resulting in a better life estimation than FVM-based S v predictions.Even though the fracture did not necessarily occur in the global S v location for most specimens, the predictions based on global values were still reasonably good.Therefore, using the global S v obtained through XCT instead of FVM-based S v for more conservative life predictions would be preferable.
In the current work, the fatigue behaviour has been investigated at one stress level below the yield stress of the material.Future work may consider investigation of fatigue behaviour at higher stress levels closer to yield, which provokes true low cycle fatigue behaviour of the material.

Conclusions
The current investigation regarding the effect of different contour themes on fatigue life for PBF-EB manufactured Ti-6Al-4 V in as-built surface conditions led to the following conclusions: • Samples manufactured by melting the contours before hatch indicated a trend of lower surface roughness and higher fatigue life.• Among the several areal roughness height parameters investigated, the S v parameter, corresponding to the deepest valley, was found to be statistically significant parameter with the best fit in affecting fatigue life.• Investigating the fracture surfaces showed that multiple cracks were primarily initiated from the as-built surface valleys, even in the presence of other near-surface defects.• Post-processing the XCT data revealed hidden surface-connected valley features.These surface-connected valleys were not included in the S v measurement by microscopy, indicating the limitation of conventional surface characterization techniques.• Fatigue life estimation using the microscopy based S v measurement had a deviation range further away from the parity line (0.52 < A/ P<0.76), which was non-conservative.In contrast, the XCT-based measurements had a deviation range spread on either side of the parity line (0.77 < A/P<1.39),indicating to be more accurate.Using XCT-based S v from global regions as initial crack size would be preferred for more realistic life predictions.

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.

Fig. 1 .
Fig. 1.Different contour themes employed for the samples in the build layout.The last character in the sample ID (shown in the Top view) represents the repetition of the respective contour theme.The geometry and location of the four-point bend specimens are shown.

Fig. 2 .
Fig. 2. Procedure to extract the peaks and valley height maps for the as-built fatigue specimens from the XCT reconstructed data.

Fig. 3 .
Fig. 3. Four-point bend specimen reconstructed from XCT data indicating the region between loading top rollers (solid blue circles).Post-fractured specimen XCT data are overlayed to establish the fracture region.Height maps of the region under stress between rollers (global) and fracture region (local) used for further surface characterisation are also shown.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 5 .
Fig. 5. Box plots showing the variation of different areal roughness height parameters for each contour theme a) maximum pit height (S v ), b) maximum height (S z ), c) arithmetical mean height (S a ), d) skewness (S sk ), and e) kurtosis (S ku ).All the surface roughness parameters have p-value < 0.05, indicating there exist a statistically significant difference in mean values for the multiple contour themes.

Fig. 6 .
Fig. 6.ANOVA multiple comparisons of the mean roughness values for the various contour themes.a) maximum pit height (S v ), b) maximum height (S z ), c) arithmetical mean height (S a ).The CL+TH contour theme (highlighted in red) has a statistically significant difference in means as compared to the contour first themes (CO, EC and SC) (highlighted in blue).The CL theme ((highlighted in grey) for S a also has a statistically significant difference in mean value compared to the contour first themes.In the case of Sv and S z , even though the CL theme (highlighted in grey) does not have a statistically significant different mean compared to all the contour first themes, it still shows a trend of increasing roughness value.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 7 .
Fig. 7. Microstructure of samples manufactured with different contour themes (a) SC (b) CL+TH.The images were taken perpendicular to the build direction.The black markings represent α laths.

Fig. 8 .
Fig. 8. Regression analysis of the relationship between fatigue life and different areal roughness height parameters.Multiple contour themes are grouped for analysing the relation between roughness parameters and fatigue life.Images a-c is plotted on a log-log scale.a) maximum pit height (S v ), b) arithmetical average mean height (S a ), c) maximum height (S z ), d) skewness (S sk ), and e) kurtosis (S ku ).Picture f) shows a Pareto chart describing the effect of different roughness parameters on fatigue life.The statistical significance at a 95 % confidence level for individual regression analysis of roughness parameter versus fatigue life has a threshold value = 2.10.

Fig. 10 .Fig. 7 ,
Fig. 10.Grayscale and false colour height maps used for XCT-based S v measurement in the region under stress (global) and fracture region (local).The images a) -e) represent one specimen from each contour theme.Negative values in the false colour maps indicate valleys.Markings in brown refer to the global region, and markings in purple pertain to the local region.sign indicate the location of the maximum (deepest) valley feature.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) authorship contribution statement K. Thalavai Pandian: Writingoriginal draft, Methodology, Investigation, Formal analysis, Conceptualization.E. Lindgren: Writing review & editing, Software, Methodology.S. Roychowdhury: Writing review & editing, Methodology, Formal analysis.M. Neikter: Writing review & editing, Supervision.T. Hansson: Writingreview & editing, Supervision, Conceptualization.R. Pederson: Supervision, Project administration, Funding acquisition.