Size-dependent stochastic tensile properties in additively manufactured 316L stainless steel

Journal Pre-proof Size-Dependent Stochastic Tensile Properties in Additively Manufactured 316 L Stainless Steel Ashley M. Roach (Investigation) (Writing - original draft), Benjamin C. White (Investigation) (Visualization) (Writing - review and editing), Anthony Garland (Formal analysis), Bradley H. Jared (Writing review and editing), Jay D. Carroll (Conceptualization), Brad L. Boyce (Conceptualization) (Investigation) (Writing - review and editing) (Supervision) (Project administration) (Funding acquisition)

PII:

S2214-8604(19)31573-8

DOI:

https://doi.org/10.1016/j.addma.2020.101090

Reference:

ADDMA 101090

To appear in:

Additive Manufacturing

Received Date:

10 September 2019

Revised Date:

19 November 2019

Accepted Date:

23 January 2020

Please cite this article as: Roach AM, White BC, Garland A, Jared BH, Carroll JD, Boyce BL, Size-Dependent Stochastic Tensile Properties in Additively Manufactured 316 L Stainless Steel, Additive Manufacturing (2020), doi: https://doi.org/10.1016/j.addma.2020.101090

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Size-Dependent Stochastic Tensile Properties in Additively Manufactured 316L Stainless Steel Ashley M. Roacha, Benjamin C. Whitea, Anthony Garlanda, Bradley H. Jareda, Jay D. Carrolla, Brad L. Boycea,* a

Materials, Physical, and Chemical Sciences Center, Sandia National Laboratories, Albuquerque, NM 87185-0889 *Corrosponding Author: [email protected]

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ABSTRACT Recent work in metal additive manufacturing (AM) suggests that mechanical properties may vary with feature size; however, these studies do not provide a statistically robust description of this phenomenon, nor do they provide a clear causal mechanism. Because of the huge design freedom afforded by 3D printing, AM parts typically contain a range of feature sizes, with particular interest in smaller features, so the size effect must be well understood in order to make informed design decisions. This work investigates the effect of feature size on the stochastic mechanical performance of laser powder bed fusion tensile specimens. A high-throughput tensile testing method was used to characterize the effect of specimen size on strength, elastic modulus and elongation in a statistically meaningful way. The effective yield strength, ultimate tensile strength and modulus decreased strongly with decreasing specimen size: all three properties were reduced by nearly a factor of two as feature dimensions were scaled down from 6.25 mm to 0.4 mm. Hardness and microstructural observations indicate that this size dependence was not due to an intrinsic change in material properties, but instead the effects of surface roughness on the geometry of the specimens. Finite element analysis using explicit representations of surface topography shows the critical role surface features play in creating stress concentrations that trigger deformation and subsequent fracture. The experimental and finite element results provide the tools needed to make corrections in the design process to more accurately predict the performance of AM components.

1. INTRODUCTION

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Key Words: Additive manufacturing; Laser powder bed fusion; Surface roughness; Feature size; Strength; Elastic modulus; Ductility; Crystallographic texture, 316L stainless steel

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Recently there has been considerable advancement in the field of metal additive manufacturing (AM), both in terms of the technologies used, and the diversity and volume of applications for AM parts. Once used almost exclusively for prototypes and small non-load bearing one-off structures, metal AM is beginning to be used in mainstream mass production [1-3]. Alongside this advancement, and increasing use, have been numerous efforts to qualify structural parts, which has proven to be a tremendous challenge [4, 5]. While many metal AM processes have similar capabilities and challenges, the current study is interested in laser powder bed fusion (LPBF), also known as selective laser melting (SLM) [6]. In this process a laser is scanned over a bed of stationary powder, melting the powder in the laser path to form a solid cross section of the part. A new layer of powder is then spread over the part, and the 3D part is built one layer at a time. The mechanical properties of the final part are dependent on many factors including: powder characteristics [7], laser power, velocity and scan strategy [1, 8-10], build orientation and location [11-13], post processing [11, 12], and surface roughness [14-17]. Within complex geometries, the dynamic conditions for melting, solidification and reheating can vary from location to location, making it difficult to obtain uniform properties with fixed printing parameters. The large number of parameters, some of which are difficult to control, creates well-documented challenges with consistency in mechanical properties [1, 4, 5, 7, 11-13, 18-20]. AM components can exhibit variations in mechanical properties between different machines using the same nominal conditions, and even among samples printed in the same batch on the same machine [11, 19]. In a round robin study by Ahuja [11], the ultimate strength of specimens was found to vary by as much as 50% between vendors, and by 30% within some vendors, with ductility showing considerably more drastic differences. This variation makes it necessary to adopt a statistically rigorous approach to component qualification. To accommodate large numbers of samples, streamlined high-throughput testing can be implemented to improve efficiency. By using a drop-in grip configuration and non-contact digital image correlation (DIC) extensometers, large data sets of up to 1000 samples can be obtained in a matter of hours [18, 21]. Such studies can provide the statistical basis that is needed for the design of critical components and can provide insight into rare worst-case defects that occur in only a few percent of samples [21]. 1

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Processing parameters, particularly input energy, determine part microstructure [10, 22, 23]. Just as important as the energy put into the part, however, is the conduction of this heat through and away from the part. Much theoretical and computational work has explored the heat flow through AM parts, which is primarily influenced by the cross section and the height from the build plate of the feature [24-27]. In particular, Mukherjee has shown computationally that cooling rates and melt pool volumes are effected not only by heat input and height of the build, but by the number of parallel laser scans [27]. This suggests that the width of features could be expected to change the thermal history of the feature, and therefore its microstructure. The freedom to design complex structures afforded by AM results in components that can contain a wide range of feature sizes. LPBF can produce features as small as 100 µm [28], and many components such as lattice materials [29], biological implants [30], and heat exchangers [31], benefit from such features. Features on this scale are often made by a single pass of the laser, so input energy has a direct effect on the thickness of the feature. However, altering the input energy may create key-hole, lack of fusion or porosity defects [32, 33]. In many cases processing parameters cannot be changed during the build, so parameters that may be ideal for small features may not work as well for bulk structures and vice versa, making it necessary to investigate the effect of size on the performance of the component. Brown et al. have shown a trend of decreasing mechanical performance with decreasing wall thickness in both LPBF produced 304L, and Electron Beam Melting Ti6Al4V [34]. While Brown et al. indicate there is a likely a strong size effect, more work is needed to understand root causes, and to address statistical variations as a function of feature size. It is unknown whether the large variation in mechanical properties inherent in AM components becomes more or less pronounced when the test specimen size decreases. To address this concern, the current study employed a highthroughput testing strategy to investigate the mechanical properties of LPBF printed 316L stainless steel spanning the typical range of component feature sizes. Additionally, finite element analyses (FEA) were performed to demonstrate the role of surface topography in stress concentrations that lead to sample deformation and subsequent failure.

2. METHODS

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Tensile specimens of varying gauge volumes were manufactured by laser powder bed fusion and tested to failure using a high throughput tensile testing process. Five sizes of tensile specimens with gauge volumes ranging from 0.256 mm3 to 977 mm3 were manufactured, with at least 19 samples per size, and 153 specimens tested in total. These sizes were chosen to replicate the printable range of failure-critical features often found in additively manufactured geometries. The sample geometries shown in Figure 1 conform in the gauge section and transition radius to ASTM E8 guidelines for dimension ratios, with pin or clamp grip sections replaced by a 45o angle drop in grip configuration. This sample geometry was linearly scaled to produce the five different sample sizes dimensioned in Table 1. Table 1:Nominal Sample DimensionsSince no overhangs exceed 45o this geometry is readily printable in all sizes, and orientations without supports, reducing post build sample preparation time. Furthermore tensile tests using drop in grips are much quicker to set up and allow for automated high-throughput testing, which is critical when the number of samples being tested reaches into the hundreds [18, 21]. These studies, show this sample geometry to be suitable for high throughput testing, quickly producing results consistent with manufacture specifications for wrought material [18] and very few grip failures.

Figure 1: (a) Tensile specimen build orientation and layout, and (b) tensile specimen geometry

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Two identical build cycles, each with all sizes printed on a build plate, were fabricated from 316L stainless steel, also known as UNS S31603 or WNR 1.4404, using a ProX DMP 200 (3D Systems) laser powder bed fusion printer. While the part spacing in Figure 1 is quite close, the microstructure was found to be consistent within each sample, and between sample sizes, indicating little effect of part spacing. The powder layers were nominally 30 µm thick, and the average powder diameter (D50) was 16.7 µm, with a 10% powder size distribution (D10) of 8.2 µm, and a 90% particle size distribution (D90) of 27.6 µm. The nominal laser power was programmed for 103 W, with a 100 µm beam diameter and a scan velocity of 1.4 m/s. The laser used a 3D systems hexagon raster scan pattern with 50 µm hatch spacing. The chamber was filled with argon cover gas and contained approximately 1000 ppm oxygen. These parameters are baseline values recommended by the manufacturer and had proven to work well over a range of previous builds. Walls were built around the smaller tensile samples shown in Figure 1 to protect them from the powder recoater. All the samples were tested in the as-built condition without any post processing, surface finishing or thermal treatment.

Thickness [W] (mm) 0.40 0.6 1.0 2.5 6.25

Length, [4W] (mm) 1.6 2.4 4 10 25

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W=0.4 W=0.6 W=1.0 W=2.5 W=6.25

Width, [W] (mm) 0.40 0.6 1.0 2.5 6.25

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Table 1:Nominal Sample Dimensions

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After printing, tensile samples were cut from the build plates by wire electrical discharge machining. Metallography was conducted on the longitudinal cross section of a single sample from each specimen size using standard grinding and polishing procedures. Porosity was calculated from the area fraction of pores optically measured on the metallography cross sections. Grain size and crystallographic texture were quantified with electron backscatter diffraction (EBSD). An Oxford EBSD system was used with a step size of 2 µm for the smallest size (W=0.4 mm), and 3 µm for the other sample sizes. Standard functions available in the Matlab toolbox MTEX were used to calculate the texture index and average grain sizes of each specimen size. The same metallography cross sections were then used for Vickers microhardness testing, using a load of 100 g, and a 15 sec dwell. Six hardness measurements were taken along the gauge length of a specimen from each size. A representative tensile specimen from each specimen size was characterized by micro-computed tomography (CT) using a Zeiss Xradia 520 Versa system. Because the largest sample was approximately 4000 times the volume of the smallest sample, the voxel size was varied from 0.89 µm to 1.73 µm, in order to maintain practical scan times. While the CT data is used primarily to qualitatively asses the sample shape, these voxel sizes should still reveal any significant internal porosity and provide a detailed 3D maps of the sample surface topography. A voltage of 160 kV was used to image the larger samples, which was reduced to 140 kV for the smallest (W=0.4) sample. The surface roughness of the specimens was characterized from a longitudinal CT cross section at the mid plane of the specimen. The edge was extracted from the 2D image, and an average surface roughness calculated from the digitized profile. The width and thickness of every specimen was measured using a Keyence IM-6000 optical measuring microscope, also screening out excessively warped specimens. Monotonic tensile tests were performed on an MTS load frame, at a strain rate of 1.25x10-2/s. The samples were loaded to 2% strain, unloaded to zero load to measure the unloading modulus, and then re-loaded to failure. Commercial 2D Digital Image Correlation (DIC) software, VIC-Gauge, by Correlated Solutions Inc., was used to measure virtual extensometer strain without contacting the samples, providing a consistent method of strain measurement across all five sample sizes. The virtual gauge length was selected to be the entire gauge length of the sample (4W) from fillet to fillet. DIC images were acquired with a Point Grey Grasshopper camera (model GS3-UR-41C5M-C) with Edmund Optics lenses scaled such that the gauge lengths filled >50% of the field of view. The two-point virtual extensometer with this set up had a root mean square strain noise floor of ~0.0002 mm/mm. Finite element analysis (FEA) was used to corroborate and interpret the experimental observations. The effect of sample surface roughness was explicitly modeled by extracting the surface features from a CT slice at the mid-plane of the specimen. This surface was then used to create an extruded 2.5D model that could be analyzed using Sandia’s computational mechanics suite, Sierra [35]. A multilinear elastic-plastic hardening model with failure that has been used extensively in other studies [36-38]was used to simulate the tension test to complete failure of the part. 3

3. RESULTS 3.1 Microstructure Characterization

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HR-EBSD grain orientation maps containing a total of 18.5 million points are presented in Figure 2. While not shown, metallography did not reveal any significant difference in precipitates, or grain boundary segregations. All sample sizes have a [001] texture in the build direction, similar to 316L microstructures from LPBF reported in previous work [39-41]. An inverse pole figure quantifying this texture is given for the W=6.25 specimen in Figure 2b and is representative of the other specimen sizes. Feature size and processing parameters can produce complex thermal gradients that lead to gradient grain structures [25]. However, for the processing conditions used in this study there is little, if any, detectible gradient in grain size, orientation, or aspect ratio between the center and the edge of the specimens. The grain structure at the immediate surface of the samples shows a thin (<100 µm) region of refined grains likely caused by grain nucleation from partially melted particles. Subsequent analysis however suggests that the mechanical response in this region is dominated by the geometric contributions of surface topography.

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Figure 2: a) EBSD maps of the crystallographic grain structure of each sample size, at a common scale, b) Inverse pole figure for the W=6.25 sample with respect to the build direction

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Figure 3 summarizes the microstructural parameters as well as microhardness between the different specimen sizes. The grain aspect ratio is calculated as the ratio of major to minor axes of an ellipse that has been fit to each grain and then averaged over all grains in the specimen. The texture index quantifies the degree of anisotropy, with an index of 1 representing a fully isotropic grain structure, and an index of infinity a single crystal [42]. The texture index is calculated from the square of the orientation distribution function integrated over orientation space (Eq. 1). 𝐽 = ∮(𝑓(𝑔))2 𝑑𝑔

Eq. 1

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The properties shown in Figure 3 are relatively consistent between the specimen sizes, and very consistent within each specimen as a function of height. The grain size, texture index, and surface roughness may increase marginally as specimen size increases, before dropping back down, though this trend is relatively slight and could be influenced by the smaller number of grains measured in the W=0.4 and W=0.6 samples. The microhardness however is nearly the same for all samples suggesting that what minor differences in microstructure are present do not appreciably affect the mechanical properties.

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Figure 3: Texture index, grain size, grain aspect ratio, and microhardness of the five sample sizes normalized by the W=6.25 specimen. The values for the W=6.25 specimen are given in the legend.

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3.2 Mechanical Response High throughput tensile tests were performed to probe the mechanical response, and statistical variations as a function of specimen size. No statistically significant variation in tensile properties between builds of the same size specimen were observed, so the data from both builds has been combined into one data set. The number of specimens tested and the property statistics are included in Table 1 of the Appendix. While the microhardness (Figure 3) is quite consistent for all sample sizes, the stress strain plots given in Figure 4 show significant differences in strength between the sample sizes. Also apparent is the wide spread in elongation to failure for all sample sizes, which is characteristic of AM material. The largest sample sizes, W=2.5 and W=6.25 generally agree with yield, UTS and elongation values for machined specimens found from the literature, though as previously noted the literature shows significant variations in properties between sources [12, 13, 15].

Figure 4: Stress-strain plots for all tensile samples of all sizes

The yield strength, ultimate strength (UTS), and elastic modulus, plotted in Figure 5a-c, all decrease significantly with decreasing sample size. The smallest samples, W=0.4, exhibit effective strengths and stiffnesses of only ~50% of the bulk samples (W=6.25). In absolute terms, the variability in strength increases slightly as the sample size decreases, however in relative terms this increase in variation is significant. The elongation to failure of the samples (Figure 5d) show little differentiation between sample sizes, instead showing substantial sample-to-sample variation

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within each size, as has been observed elsewhere [18, 21]. Since elongation to failure is a dimensionless quantity, it is not affected by errors in area measurements like strength and stiffness, parameters dimensioned in N/mm2. Statistical Tukey analysis, presented in the Appendix, indicated that only the W=6.25 specimen size had a statistically distinct elongation distribution. Subsequent fractographic analysis was not able to determine a clearly distinct failure mechanism for the W=6.25 mm sample population. However, unlike the other specimen sizes, most of these largest samples failed at nearly the same location in the gauge section. This suggests that, for both builds, there was a particular build layer that produced ductility-limiting flaws. These defects however occurred at different heights for each build plate, and could not be correlated with any features found in metallography of EBSD. This type of defect behavior (though not necessarily this specific cause) is related to sample size, as larger samples are more statistically likely to sample the entire distribution of flaws, including the less common larger flaws. Smaller specimens on the other hand sample only a fraction of the flaw population, resulting in some samples with virtually no flaws, and some samples with large flaws relative to the sample size, increasing the variability between specimen.

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Figure 5: Tensile properties as a function of sample size. a) yield strength, b) ultimate strength, c) elastic modulus, d) elongation to failure.

The maximum likelihood estimates of Weibull three- parameter cumulative probability distributions for ultimate tensile strength are shown for all five specimen sizes in Figure 6 as determined using Minitab statistical analysis software. Among 15 common distributions, the 3-parameter Weibull provided a best fit as determined using an Anderson-Darling goodness of fit. This distribution had also proven effective in previous statistical datasets [21]. This graphical representation emphasizes the systematic trend in ultimate strength distribution as a function of specimen size. The kink in the W=6.25 mm dataset suggests a subtly bimodal response, which may indicate two distinct flaw populations. This is likely related to whatever build flaws caused the consistent failure location observed in the W=6.25 samples. Setting aside the bimodality of W=6.25, there is a trend of increasing distribution breadth for smaller specimen sizes.

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Figure 6: Cumulative probability of UTS at failure for each specimen size.

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Since the intrinsic microstructure and microhardness show little variation between specimen sizes, the observed trend of decreasing strength and modulus with specimen size suggests an extrinsic source. A likely explanation is that the surface roughness obfuscates the precise determination of the true load-bearing area. A surface effect explanation is consistent with the strength and elastic modulus asymptotically approaching a constant value at larger sample sizes, as the surface area to volume ratio decreases (Figure 5a-c). Such an issue has been described previously [43], and is analyzed in more detail in the discussion. However even the largest specimens, where surface effects are minimal, exhibit modulus values that are substantially lower than the accepted Young’s modulus of ~193 GPa for wrought 316L. This can be attributed to the [001] texture in the loading direction of all the samples, which is the most compliant orientation. For austenitic (FCC) stainless steel the [001] direction has a modulus of 101 GPa, approximately half of the isotropic polycrystalline value [44]. Prior work has shown that the [001] direction is a preferred growth orientation for LPBF, particularly with high energy input [39-41]. A study by Niendorf et al. characterizing the same alloy and manufacturing process as the current paper, showed that very strong [001] textures could be produced with high energy input, resulting in elastic modulus values half that of the samples with more isotropic grain structure [39]. The effective elastic modulus produced by crystallographic texture can be roughly estimated from the single crystal elastic constants [45], and the crystal orientation distribution obtained from EBSD [46]. While there is no uniformly agreed upon method for this homogenization, the Voight (Eq. 2, [47]) and Reuss approximations (Eq. 3, [48]) are useful because they give upper and lower bounds for the polycrystalline modulus respectively. The Hill approximation (Eq. 4, [49]) meanwhile is a commonly used simple average of the two. The Voigt and Reuss equations are given in Eq. 2-3, in forms compatible with EBSD data [50]. The subscript SX refer to the single crystal stiffness/compliance matrices, and f(g) is the orientation distribution function obtained from EBSD, all integrated over the orientation space. ̅̅̅̅𝑉𝑜𝑖𝑔𝑡 = ∮[𝐶]𝑆𝑋 ∙ 𝑓(𝑔) ∙ 𝑑𝑔 [𝐶]

Eq. 2

̅̅̅̅𝑅𝑒𝑢𝑠𝑠 = ∮[𝑆]𝑆𝑋 ∙ 𝑓(𝑔) ∙ 𝑑𝑔 [𝑆]

Eq. 3

̅̅̅̅ [𝐶]𝐻𝑖𝑙𝑙 = 1⁄2 ([𝐶]𝑉𝑜𝑖𝑔𝑡 + [𝐶]𝑅𝑒𝑢𝑠𝑠 )

Eq. 4

These approximations give upper and lower bounds for the microstructures in Figure 2 of 159 GPa and 134 GPa. The Hill average of 146 GPa is remarkably close to the average value of 143 GPa observed in the largest (W=6.25) samples. While these approximations must be taken with some caution, they clearly demonstrate the important role of texture in the elastic moduli observed experimentally. In addition to the microstructural texture component, small values of porosity have also been shown to have an outsized effect on the elastic modulus of LPBF 316L [41], and may be a secondary contributing factor in this case as well. 3.3 Micro-computed tomography

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Micro-computed tomography (CT) scans of representative examples for sizes W=0.4, W=0.6 and W=2.5 sizes are presented in Figure 7. The W=2.5 size sample shows larger pores, with the largest >100 µm, however the smaller samples contain similar levels of total porosity (Figure 8) with more smaller pores. The decreasing max pore size with decreasing sample size could be due to a sample size effect that is commonly seen in smaller samples, or it could be caused by the thinner geometry itself. A potential example of the statistical size effect phenomenon is that some small samples (400 µm wide/thick) may have contained large >100 µm pores, but the flaw to sample size ratio may have caused them to fail during the print. About half of the smallest samples (W=0.4) failed geometric inspection, and some of them failed entirely during printing, while only a few of the W=0.6 samples, and none of the larger samples failed geometric inspection. Some print failures were observed in this smallest size only, but no direct causation could be attributed, and many factors play a role in print failures. While high throughput micro CT is not yet practical, the large number of samples mechanically tested allow us to capture this statistical variance.

Figure 7: CT images for the W=2.5, W=0.6, and W=0.4 size samples. Left column: 3D Render, middle column: longitudinal cross section, Right column: loading cross section

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The surface roughness and porosity for each sample is given in Figure 8, and are relatively constant for all specimen sizes. The surface roughness (Ra) was digitally measured from the edge of the CT longitudinal cross sections shown in Figure 7b, 7e, and 7h. Because the surface roughness is driven by the powder size and laser parameters, which were both constant for all sample sizes, it is not surprising that the surface roughness is similarly consistent between the specimen sizes. While much effort has been spent characterizing and reducing the porosity of AM components in the literature, the surface roughness clearly becomes a more substantial issue as the sample size decreases. Additionally, it is worth noting that from fracture mechanics theory, surface flaws are known to be substantially more detrimental than equivalent internal flaws.

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Figure 8: Surface roughness and porosity for each specimen size, normalized by the W=6.25 value given in the legend.

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The surface roughness becomes such a dominate feature of the smaller samples that it obscures our ability to properly dimension these small features. While the W=2.5 specimens (Figure 7a-c), shows a square cross section with relatively minor surface features, the W=0.4 sample (Figure 7h-i), is so dominated by the surface roughness, that it is impossible to ascertain the nominally square cross-section. This type of roughness induced geometric error has also been shown in CT data from lattices [51]. Clearly a mechanical measurement, which measures in 1D from the peak on one side to the peak on the other, would greatly overestimate the true thickness of the sample. From the 3D render however it can be seen that even a two-dimensional optical measurement, capable of extracting average, min/max, etc, would still not be able to capture the true 3D surface topography.

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3.4 Finite Element Modeling

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To better understand the cause of the reduced mechanical performance of the smaller specimens, finite element models were generated based on the CT cross sections. The longitudinal center cross sections from the CT data, (Figure 7b, 7e, and 7h) were used as the base geometry. A python script was written to extract the surface features from the CT cross section using standard image analysis edge detection algorithms. The edge geometry was then used to build an extruded 2.5D model, as outlined schematically in Figure 9. Some surface detail is lost during the edge detection, meshing and transfer pipeline, however as a first order approximation this analysis provides useful insights.

Figure 9: Process flow for edge extraction and surface modeling

A multilinear elastic-plastic hardening model with failure, used extensively in other studies [36-38], was used to simulate the tension test to complete failure of the part. The plastic hardening behavior was based on previous experimental results of LPBF 316L [38]. As a control, a W=6.25 reference test specimen (the “bulk” specimen) with smooth walls was also evaluated using FEA. The model for the rough 0.4 mm width specimen is shown in Figure 10. The FEA results illustrates that the surface roughness of the test specimen produces stress concentrations which serve to trigger early yielding, reduce ultimate strength and drive premature fracture.

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Figure 10: Evolution of damage initiating from stress concentration

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The FEA estimate for UTS is compared to the experimental data in Figure 11 and follows the same trend observed experimentally. Since the samples were tested in the as printed state, it is possible that residual stresses alter the effective properties, however the FEA was conducted without any initial (residual) stress, and shows that the geometric contribution from surface roughness alone is able to capture the majority of the size effect behavior. For the purposes of the present study, the current simplified FEA is sufficient to illustrate the semi-quantitative effects of the stressconcentrating surface roughness features. Future analysis efforts could be refined by modeling 3D surface roughness, or by parameterizing the surface roughness such that meaningful statistics can be generated from representative instantiations of surface roughness.

Figure 11: Comparison of experimental data with FEA results explicitly modeling the surface roughness.

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4. Discussion

Traditionally, materials science is viewed through the lens of process-structure-property-performance relationships. The material property aspect is viewed to be an intensive feature of the material, and does not itself depend on the size, or shape of the material present. However, in the case of additive manufacturing, both the intensive material properties and the effective material properties (structural properties) are intrinsically coupled to the shape and size of the features. In general, AM components may have internal microstructural variation that depends on feature geometry, and as a result, their intensive properties can vary within the material from voxel to voxel and from one geometry to another. A component printed at one scale may have different microstructure/property gradients than the same component printed from the same material but at a different scale. This potentially inextricable link between geometry and properties poses a clear dilemma in design and qualification. As the concept of an intensive material property becomes not only spatially variable, but also stochastic, the problem becomes even more complex. Given all this complexity, the emphasis in qualification should focus on structural performance qualification. Feedstock and 10

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material qualification however still play supporting roles in that they attempt to maintain overall consistency from batch to batch. In the present study, the AM 316L alloy produced by laser powder bed fusion had a reasonably homogenous microstructure across specimen sizes, and as a result, the hardness, which samples the cumulative effect of this intrinsic microstructure, was constant for all sizes. Despite this uniformity in microstructure and intrinsic strength, a strong trend of decreasing effective strength with decreasing sample size was observed. While material properties are governed by the microstructure, the structural properties of components are determined by both the intrinsic material properties and the geometry of the component. Generally, these contributions can be separated through material testing, FEA, and component level testing, and the distinctions between material and structure are fairly obvious. However, as the feature size decreases, the surface roughness becomes large enough to significantly alter the geometry of the tensile specimens, blurring the line between material sample and structural component. At very small feature sizes the surface roughness begins to dominate, and microstructural differences, or even the original design geometry, can become secondary factors. While it is tempting to cast aside the geometry contribution as a problem for design engineers, this may not be possible as the geometry can be linked to the same processing parameters that control microstructure. Powder size and heat input can influence feature size and surface roughness as well as microstructure, so changing processing to optimize microstructure and material properties will also affect the geometry [28, 32, 33]. Small feature AM therefore needs to consider geometry as a fourth component to the classical materials science paradigm. 4.1 Geometric accuracy The effect of surface roughness can be subdivided into two parts: a reduction in load bearing area, and a stress concentration effect. While the reduction in load bearing area will affect all materials equally, the stress concentration effect will be more significant in brittle systems such as the Al10MgSi alloy, or certain loading scenarios such as fatigue loading. The load-bearing area problem can be characterized by simple roughness parameters or corrections to the nominal dimensions, as has been attempted in past work [18]. In this study the surface roughness was found to subtract from the load bearing area, however other sources of geometric error can be both positive or negative [52, 53]. To mitigate this, the printer or part model can be uniformly adjusted, or more complex corrections can be made by adjusting the printing parameters dynamically [34, 51]. The actual geometry of an AM feature at any one location is a function of many factors including: the nominal geometry, the dimensional tolerance of the machine, warpage from residual stress, and the roughness of the part. Some of these factors like warpage may scale with part size, however in absolute terms the magnitude of the surface roughness was found to be constant. This means that as the nominal feature size becomes smaller, the feature geometry will become dominated by surface roughness. At the extreme end, as the feature size approaches the scale of the surface roughness, a roughness valley may cut all the way through the part, or far enough through that the part cannot stand up to the powder wiper, and the part fails to print. In reality print failures are coupled events that depend on the process, the machine and the feature. Since gross geometric effects are seen in both the strength and the elastic modulus, it is interesting to divide the two to produce a normalized, non-dimensional yield strength shown in Figure 12. The yield strength, and elastic modulus measured for each sample were used in this normalization. Like elongation to failure, this parameter is dimensionless, so it should not depend on flawed measurements of cross-sectional area, i.e. a constant bias would cancel out. As expected, there is no discernable trend in this parameter as a function of specimen size. Furthermore, if the scatter in modulus and yield strength are assumed to be due to the error in cross-sectional area measurements, then the scatter in the normalized yield strength should approach zero. However, because this is not the case, it appears that area reduction is not the whole story, and that other factors, notably stress-concentration contributions from the surface roughness are affecting the specimen response.

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Figure 12: Effective yield strength normalized by effective elastic modulus.

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The problem of surface topography specific stress concentrations is more difficult to understand because it requires much more detailed information on the exact contour of the surface. Measuring the surface profile of AM parts is challenging because they contain overhangs and crack like features that are difficult or impossible to capture with physical profilometry, or line of sight optical surface measurement techniques. Fortunately, CT data does not suffer from these problems, and is only limited by the resolution of the instrument. More detail on metrology of AM components can be found in the literature [52, 54-56]. Once the surface profile of the features has been obtained, FEA can be used to estimate stress concentrations quite accurately. This process however is cumbersome, and since stress concentrations tend to be a weakest link problem, potentially subject to large statistical variance. While the stress concentration problem can be quite significant for some surface topographies and brittle materials, for ductile materials, and closely spaced uniform surface features the stress concentration effect will not be as severe. Rather than the surface features disrupting the flow of stress through the sample, if they are spaced frequently enough, there will be little stress carried near the surface at all. Instead the surface stress concentrations will act as a reduction in effective load bearing area. Stress concentration solutions for an infinite row of semicircular edge notches compiled by Peterson show that the stress concentration decreases both as the notch spacing decreases, and somewhat counterintuitively also as the notches become larger compared to the plate width [57]. This line of reasoning indicates that while originally assumed to be distinct, the load bearing area reduction and stress concentration effect may in fact be linked, though not the same. Because stress concentrations may be reducing the effective load bearing area below the surface it may be impossible to measure the true load bearing area directly, irrespective of the measurement technique. 4.2 Design Implications

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Though surface roughness has been well documented as a problem in AM since its inception, the full implications of the problem have not been fully realized. While a simple knock down factor due to surface roughness on the strength (yield, ultimate, or fatigue) is easy to accommodate by simply designing under this threshold, the effect of roughness on the stiffness of printed parts is perhaps more important because it affects the design at any level of loading. Some applications, such as vibration isolation or damping, are not limited by strength but rather derive their performance solely from the stiffness of the part. In this study the effective stiffness of the 0.4 mm samples was found to be half that of the bulk samples, because of a surface roughness induced reduction in load bearing area. The stiffness will be further reduced in bending loading since the flexural rigidity goes with the dimension to the third or fourth powers instead of length squared as in the tensile stiffness. If the smallest sample in this study were loaded in bending (I=1/12W4) its flexural stiffness would be only one quarter that of the bulk samples. On top of the surface roughness reduction, the microstructural texture from the AM process may add as much as another factor of two reduction to the stiffness. Taken together it is possible to have an effective tensile stiffness on the order of a quarter of the accepted book value, or one eighth of the expected flexural rigidity. Because the dimension reduction affects tensile and bending loading differently it cannot be fully accounted for by simply using an effective elastic modulus, though modulus adjustments are simple to implement and have been shown to greatly increase the accuracy of FEA predictions [29]. Subtracting a surface layer from the nominal design dimension to give an effective thickness is proposed to be a more accurate correction. The microstructural component of the stiffness reduction however must still be accounted for by using a reduced elastic modulus, or preferably an 12

anisotropic elastic model. Both corrections are necessary to accurately predict structural responses in parts that are subjected to complex loading. 5. SUMMARY AND CONCLUSIONS

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The effective strength and stiffness of as printed LPBF 316L specimens was found to decrease dramatically as the specimen size decreased. Through analysis of microstructure, the mechanical response of statistically relevant sample sizes, and the use of finite element modeling, this performance reduction can be attributed to surface roughness effects. The most significant conclusions are listed below: 1. The surface roughness was found to reduce mechanical performance via two mechanisms: decreasing the effective load bearing area and creating stress concentrations. FE models created from CT data were able to accurately predict the strength of the different sized specimens. While this study was carried out using the highly ductile alloy 316L stainless steel, the size effect due to stress concentrations from surface roughness is expected to become much more significant in more brittle alloys such as Al10MgSi, or in other loading schemes such as fatigue loading. 2. The stochastic variation in mechanical properties increases as the sample size decreases, though this trend was not as clear as the trend in mean values. Even larger data sets are necessary to fully understand the distribution of properties. 3. In addition to the geometric size effect from surface roughness, the strong crystallographic texture from the AM process caused a significant reduction in the elastic modulus for all sample sizes. With the combined contributions from the surface roughness and microstructure, the actual tensile stiffness for the smallest specimens was found to be only ~1/3 that of the accepted value and would be expected to decrease even further in bending loading. 4. The microstructure and intrinsic material strength as measured by microhardness did not change appreciably as a function of specimen size for the 316L alloy used in this study. 5. The strength reduction, but especially the lower stiffness of smaller features, can cause large discrepancies between the predicted and actual component performance. Designers using AM components must be aware of this and take corrective measures by using an effective feature thickness and anisotropic elastic material model. It is not enough to extract true material properties and transfer them to the design procedure. AM process engineers must also include surface roughness as an equal partner with material properties when optimizing processing parameters.

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Declaration of interests

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Author-Credit-Statement Ashley M. Roach (Investigation, Writing-Original Draft), Benjamin C. White (Investigation, Visualization, Writing – Review & Editing), Anthony Garland (Formal Analysis), Bradley H. Jared (Resources, Writing – Review & Editing), Jay D. Carroll (Conceptualization), Brad L. Boyce (Conceptualization, Investigation, Writing – Review & Editing, Supervision, Project Administration, Funding Acquisition).

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.

6. ACKNOWLEDGMENTS

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The authors were supported by a Laboratory Directed Research and Development (LDRD) program. Laboratory facilities were provided in part by the Center for Integrated Nanotechnologies. The authors thank Todd Huber, James Griego, Philip Noell and Zachary Casias for laboratory support, and David Siaz for printing all the test specimens. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. The views expressed in the article do not necessarily represent the views of the U.S. Department of Energy or the United States Government. 7. REFERENCES [1] Gibson, Rosen, D. Stucker, B., Additive Manufacturing Technologies, second ed., Springer, New York, (2014). [2] T. Kellner, An epiphany of disruption: GE additive chief explains how 3D printing will upend manufacturing, G.E. Reports (2017).

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Schmidt, Developing LBM process parameters for Ti-6Al-4V thin wall structures and determining the corresponding mechanical characteristics, Phys. Procedia, 56 (2014) 90-98. [29] C.C. Seepersad, J. Allison, A.D. Dressler, B.L. boyce, D. Kovar, An Experimental Approach for Enhancing the Predictability of Mechanical Properties of Additively Manufactured Architected Materials with Manufacturing-Induced Variability, Uncertainty Quantification in Multiscale Materials Modeling (2019). [30] J. Parthasarathy, B. Starly, S. Raman, A design for the additive manufacture of functionally graded porous structures with tailored mechanical properties for biomedical applications, J. Manuf. Proc. 13(2) (2011) 160-170. [31] W.R. Schmidt, Micro heat exchanger with thermally conductive porous network, U.S. Patent No. 7871578, (2011). [32] H. Krauss, M.F. Zaeh, Investigations on manufacturability and process reliability of selective laser melting, Phys. Procedia, 41 (2013) 815-822. [33] C. Song, Y. Yang, Y. 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8. APPENDIX

Table 1. Summary of testing results for each size.

Count Mean Std Min 0.25 0.50 0.75 Max

20.0 400.8 10.69 384.1 393.5 399.5 407.0 421.3

Count Mean Std Min 0.25 0.50 0.75 Max

30.0 476.7 8.67 445.5 473.2 477.5 480.6 491.8

Count Mean Std

51.00 549.7 5.79

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Elongation to Failure [%]

Microhardness [Hv]

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19.0 347.7 16.18 312.0 338.5 344.9 359.0 371.6

Elastic Modulus [GPa] 19.0 71.4 5.10 60.5 69.5 72.0 74.1 80.6

19.0 32.9 7.26 17.1 28.6 32.9 36.9 44.9

6 232 11.2 220

20.0 93.8 13.19 83.4 87.0 88.8 92.2 133.0

20.0 30.8 7.93 13.3 29.7 32.4 35.3 41.9

6 245 13.6 232

30.0 121.0 8.32 108.2 115.1 118.2 125.8 136.6

30.0 37.0 9.27 15.6 32.1 38.5 42.7 50.3

6 232 6 224

51.00 135.41 3.45

51.00 32.09 4.67

6 229 8.2

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Count Mean Std Min 0.25 0.50 0.75 Max

Yield Strength [MPa] W=0.4 19.0 317.9 13.49 286.8 308.3 316.6 325.6 346.0 W=0.6 20.0 375.5 15.72 350.8 365.8 373.5 375.9 417.0 W=1 30.0 428.0 7.37 405.5 426.1 428.1 431.4 449.5 W=2.5 51.0 505.2 6.84

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Ultimate Strength [MPa]

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Statistic

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Table 1 provides a statistical summary of the data. An advantage of the high-throughput testing method is the high sample count N for each sample size which allows statistically robust metrics to be calculated from the results. A naïve expected outcome from the tests is that all the sizes should have the same properties without regard to size. A oneway ANOVA test can be used to test the null hypothesis that all the sizes result in the same mechanical properties. The results are in Table 2 and show that for all mechanical properties across all specimen sizes a statically significant (𝑝 < 0.05) difference in the properties exist. To explore how the groups differ from each other, a Tukey pairwise comparison test between specimen sizes for each mechanical property was calculated. While the ANOVA test shows if a particular specimen size’s properties come from a group, the Tukey test compares specimen size’s mechanical properties directly against each other. For all specimen sizes and all mechanical properties except elongation, the Tukey test resulted in rejecting the null hypothesis that different specimen sizes mechanical properties come from the same group. Figures 1 and 2 show the Tukey test results from UTS and elongation respectively.

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Count Mean Std Min 0.25 0.50 0.75 Max

33.0 565.6 13.39 536.8 550.7 571.6 575.6 579.1

494.0 500.1 503.8 508.1 51 5.9 W=6.25 33.0 524.6 10.68 499.3 516.6 527.6 532.8 541.1

124.37 133.19 135.83 137.49 142.39

14.34 29.36 32.94 35.80 38.10

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33.0 143.1 8.58 115.4 138.6 144.8 147.9 159.1

33.0 25.1 5.16 12.9 22.7 27.3 28.6 32.3

6 239 8.2 227

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536.9 546.7 550.3 554.1 561.7

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Min 0.25 0.50 0.75 Max

Table 2. ANOVA statistics

Yield 1891 6.42E126

Modulus 373 3.28E-76

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UTS 2059 1.34E128

Elongation 12.9 4.38E-09

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F score P value

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Figure A1: Tukey test results for UTS. The solid dot represents the mean. The bar is the confidence interval. No confidence intervals overlap which indicates all the sizes have statistically significantly different UTS values.

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Figure A2: Tukey test results for elongation to failure. The solid dot represents the mean. The bar is the confidence interval. Confidence bars overlap for several of the sizes which means the properties could come from the same distribution and are not statistically significantly different.

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