Influence of surface conditions and specimen orientation on high cycle fatigue properties of Inconel 718 prepared by laser powder bed fusion

International Journal of Fatigue xxx (xxxx) xxxx

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Influence of surface conditions and specimen orientation on high cycle fatigue properties of Inconel 718 prepared by laser powder bed fusion David B. Witkin , Dhruv Patel, Thomas V. Albright, Glenn E. Bean, Tait McLouth ⁎

The Aerospace Corporation, P.O. Box 92957, Los Angeles, CA 90009-2957, USA

ARTICLE INFO

ABSTRACT

Keywords: Additive manufacturing Inconel 718 High cycle fatigue Laser powder bed fusion Nickel alloys

High-cycle fatigue testing of nickel-based superalloy Inconel 718 made by laser powder-bed fusion was performed on round uniform-gauge or hourglass specimens for various specimen orientations, stress ratios and surface conditions (as-built and machined). Only surface conditions, specifically near-surface process defects, influenced fatigue properties. There was a systematic bias of the azimuthal position of crack initiation sites. Crack initiation in specimens with as-built surfaces occurred at 50 µm diameter near-surface features. These dimensions were used in conjunction with fatigue limits derived from tests suspended at 107 cycles to calculate threshold ΔK values of 2–6 MPa √m due to as-built surface conditions.

1. Introduction The use of metallic parts made by additive manufacturing (AM) in high-reliability or performance-critical applications requires understanding of mechanical properties of these materials. The majority of mechanical failures of aircraft components are due to fatigue loading environments [1], which explains the increasing interest in the highcycle fatigue behavior of a wide range of alloys prepared by additive manufacturing [2–8]. Various contributing factors to the observed fatigue behavior of AM alloys have been identified, including the presence of internal porosity or its reduction via Hot Isostatic Pressing (HIP), surface condition (specifically the use of test specimens with either machined or as-built surfaces), and specimen orientation. A recent review found that the role of specimen geometry and anisotropy of fatigue behavior is less well documented than other contributing factors [9]. A generalization may be made that the highest fatigue life (in terms of numbers of cycles before failure) is observed when AM test materials have been HIP’ed and then machined to final test specimen geometry. A significant objective in mechanical testing of AM metals is comparison of the AM version to the wrought or cast version. For the case of the precipitation hardenable nickel-base superalloy Inconel 718, recently published studies confirm these general trends but also illustrate the challenges in interpreting the literature on high-cycle fatigue. Heat treatments are critical to the properties of this class of alloys, so properties derived from materials with microstructures that are not characteristic of heat-treated parts may not be as useful to design and operation. For aerospace or other high-reliability applications, it is

⁎

expected that judicious introduction of the AM alloy into fielded systems will require recrystallization of the as-built microstructure through HIP or other thermal exposure. In fact, a recent NASA document requires this, stating the final microstructure of a metal AM part must consist of a “…predominantly uniform and non-directional recrystallized grain structure, free of remnants of the as-built structure [10].” Such transformations in Inconel 718 occur only when thermal exposure is approximately 1100 °C or higher [11,12], meaning that AM 718 alloy that is stress relieved below this temperature or directly solution treated and aged after printing will retain some characteristics of the as-built microstructure. Fatigue crack growth rates have been measured for Inconel 718 prepared by laser powder-bed fusion (LPBF) on material that received no subsequent heat treatment [13] or received only solution and duplex aging treatments without transformation of the as-built γ phase microstructure [14]. When tested with these microstructures, ΔKth and Paris regime da/dN were inferior to wrought materials. LPBF Inconel 718 that received a homogenization treatment at 1100 °C prior to solution and aging retained primary solidification features and had significantly inferior low-cycle fatigue properties compared to a conventionally processed forging [15]. These results indicate that use of LPBF Inconel 718 in aerospace or high-reliability applications will require recrystallization prior to solution treatment and aging. As a consequence, high-cycle fatigue properties based on materials that have not been recrystallized or consolidated via HIP [16–19] or not given precipitation hardening heat treatments (solution treatment and aging) [19,20] may have limited application.

Corresponding author. E-mail address: [email protected] (D.B. Witkin).

https://doi.org/10.1016/j.ijfatigue.2019.105392 Received 7 August 2019; Received in revised form 18 November 2019; Accepted 21 November 2019 0142-1123/ © 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: David B. Witkin, et al., International Journal of Fatigue, https://doi.org/10.1016/j.ijfatigue.2019.105392

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R2 se

Nomenclature An a c D F K Nf Q R

Coefficients of Basquin’s equation Crack depth Crack half length Test specimen diameter Geometric correction Stress intensity factor Number of cycles before failure Shape Factor Stress ratio = Smin/Smax

S Smin Smax ΔK ΔKth ΔKeff,t

In addition to factors intrinsic to the material itself, specimen geometry and loading conditions are likely to influence fatigue results. For example, the Metallic Materials Properties Database Development and Standardization (MMPDS) [21] discourages use of rotating beam and bending fatigue for application to the design and analysis of structures in aerospace systems and several published accounts of fatigue testing of AM 718 have relied on these test methods [22–24]. Published HCF data is relatively limited for uniaxially tested laser powder-bed fusion (LPBF) 718 that has been processed after printing using HIP and solution treatment and aging [25–27]. In this work, extensive uniaxial fatigue testing was performed in accordance with ASTM E466 [28] on Inconel 718 that was prepared by LPBF and then HIP’ed and precipitation hardened. Following MMPDS guidance, tests were performed at three different stress ratios (R = −1, 0.1 and 0.5). Results are presented for different specimen geometries (uniform gauge section and hourglass), specimen print orientations (vertical, angled, and horizontal) and surface conditions (as-built and machined). In addition to samples tested to produce S-N curves, additional sets of samples were tested at a single load condition (Smax 483 MPa and R = 0.1 or 345 ksi and R = −1) to evaluate the variation in fatigue life near 106 cycles due to as-built LPBF surfaces. In addition to specimen orientation, samples were printed with fiducial indications so that the location of the fatigue crack initiation site could be tracked with respect to the azimuthal position within the print area. Tracking this location revealed a clear bias in failure location. This is traced to the use of contour scans in combination with island or checkerboard scanning. This influence on fatigue failure initiation has not been previously described and is not attributable to factors such as unclosed porosity and surface roughness.

Coefficient of Determination for linear regression Standard error of the slope of Basquin’s equation in logarithmic form Tensile stress Minimum applied stress per test cycle Maximum applied stress per cycle Stress intensity factor range Threshold value of stress intensity factor range Effective stress intensity factor range accounting for crack closure mechanisms

2. Materials and methods 2.1. Laser powder bed fusion settings All samples were fabricated on a Concept Laser M2 Cusing model using a hatch spacing of 105 µm and a layer thickness of 30 µm. Part interiors were made with a laser power of 180 W and scanning speed of 600 mm/s. Each part was built with two contour scans at a laser power of 160 W and a scanning speed of 300 mm/s for the outer contour and 350 mm/s for the inner contour. The contour settings typically give a vertical surface roughness as Ra on the order of 5–7 µm. Samples were printed under an argon atmosphere. Additional details concerning the processing of alloy 718 in this printer have been previously reported [29,30]. Samples were designed based on guidance found in ASTM E466 for specimen design. Most specimens were tested with an as-printed uniform gauge length of 12.7 mm, gauge diameter of 6.35 mm and a transition radius of 50.8 mm (Fig. 1). Samples that were tested with machined surfaces were printed to slightly oversize dimensions (e.g., approximately 0.5 mm larger gauge section diameter) and machined to final dimensions that were the same as the as-printed specimens. Final, as-tested geometry of these specimens is illustrated in Fig. 1a. All horizontally oriented samples were machined to final test geometry. As shown in Fig. 2, round specimens based on ASTM E466 require build supports during printing and cannot be tested with asprinted surfaces. Vertically-built (henceforth, vertical) specimens were built without supports and tested with either as-built surfaces or with machined surfaces for comparison to horizontally-built (henceforth, horizontal) specimens that required machining. Specimens built at an angle (henceforth, angled) were inclined at 30° away from vertical and were built without supports in the gauge section. Illustrations of the build plates are shown in Fig. 2. The angled specimens were oriented to

Fig. 1. Geometries of uniform gauge specimen (a) and hourglass specimen (b). All units are mm. 2

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Fig. 2. Schematic of specimen orientations on build plates for vertical (left), horizontal (middle) and angled (right) specimens. Supports are shown for horizontal specimens and at the base of angled specimens.

two different directions, which in additive manufacturing nomenclature is B−30 and B+30 for left-pointing and right-pointing specimens, respectively, on the right-most image in Fig. 2 [31]. An additional set of samples was prepared using an hourglass profile with a continuous radius of 50.8 mm and a minimum gauge diameter of 6.35 mm (Fig. 1b). A final build plate consisting of twenty-four vertical specimens was tested with as-built surfaces at one of two loading conditions intended to correlate with one million cycles to failure at either R = 0.1 or −1 based on the S-N curve. This was at Smax approximately 10% higher than the estimated fatigue limit at 107 cycles based on the initial testing to define an S-N curve for this specimen orientation and surface condition.

3. Results 3.1. Microstructure Examples of the final microstructure of the test materials after all heat treatments are shown for a vertical specimen in Fig. 3. This microstructure is representative of the material regardless of original specimen orientation. Fig. 3a and 3b show the interior of the specimen for X-Y (normal to the build direction) and Z plane (parallel to the build direction) sections, respectively, and Fig. 3c shows the edge of the printed specimen at the as-built surface. At higher magnification of a Z plane section (Fig. 3d), annealing twins and favorable precipitation of delta phase (Ni3Nb, orthorhombic) at grain boundaries can be seen. These metallographs show that the microstructure is equiaxed in both sections after recrystallization during HIP and subsequent solution treatment and aging. Fig. 3c shows that the microstructure at the edge of the specimen (where fatigue cracks initiate) is similar to the interior. A comparison of the microstructure in vertical sections of an angled specimen and vertical specimen that were each tested at R = 0.1 and Smax 621 MPa is shown in Fig. 4. These include the as-built surface and show the respective microstructures within a few 100 μm’s of the fracture surface near the fracture origin (Nf = 894 K cycles for vertical and 979 K cycles for angled) illustrating the similarity for different specimen orientations and the general lack of texture or grain aspect ratio with respect to the build direction.

2.2. Post-printing heat treatment LPBF materials were Hot Isostatically Pressed and heat treated at commercial suppliers. The HIP cycle consisted of three hours at 1163 °C and 100 MPa. Heat treatment was performed according to AMS 5663, which includes a solution anneal at 954 °C followed by quenching, then dual-temperature precipitation aging at 718 °C for 8 h, followed by furnace cooling to 621 °C and holding until a combined aging time of 18 h was achieved. Although tensile testing was not part of this investigation, room-temperature tensile properties of Inconel 718 produced on the same Concept Laser M2 and HIP’ed and heat treated using the same schedules as the fatigue specimens has been previously reported for vertical, horizontal and angled specimens [32]. The inclination of the angled tensile specimens was 45° (B + 45) from the Z axis, while for fatigue specimens the corresponding inclination from vertical was 30° (B−30 and B+30). These results (Table 1) show that there is a small difference in room temperature tensile properties and elastic modulus between vertical orientation and angled or horizontal.

3.2. Fatigue test results: S-N curves Load-controlled fatigue data are presented as S-N curves in Figs. 5–7 to emphasize comparisons of interest. Fig. 5 shows results for vertical specimens at three stress ratios with as-built surfaces for uniform gauge specimens and two stress ratios for hourglass specimens. Data for test specimens with machined surfaces are shown in Fig. 6, including vertically oriented specimens at R = 0.1 and horizontally oriented specimens at R = −1, 0.1 and 0.5. Data for vertical specimens with as-built surfaces at R = 0.1 are reproduced to show comparison between asbuilt and machined surfaces. Finally, data for test specimens built at an angle (30° from vertical, combining both B−30 and B+30 specimens) with as-built surfaces are plotted in Fig. 7 along with the vertical specimen data. For each case where test data allows, a fatigue limit is estimated as the approximate maximum stress for a given condition associated with run out at 107 cycles without failure; these values are summarized in Table 2. It is emphasized that this limit is based on the

2.3. Fatigue testing All fatigue tests were performed on an Instron servo-hydraulic load frame controlled by Instron WaveMatrix software. Specimens were fixed with hydraulic wedge grips. Tests were run at a frequency of 40 Hz and stress ratios of −1, 0.1 or 0.5. Tests reaching 107 cycles without specimen failure were suspended. A single cycle was counted as consisting of beginning at maximum load, unloading to minimum load, and returning to maximum load.

Table 1 Room temperature tensile properties of laser powder bed fusion Inconel 718 build using identical equipment, build parameters and heat treatments as the current study [32]. Specimen Orientation

Yield Strength (MPa)

Ultimate Tensile Strength (MPa)

Elastic Modulus (GPa)

Elongation (%)

Vertical Angled (B + 45) Horizontal

1034 ± 1.4 1062 ± 1.4 1055 ± 2.1

1365 ± 1.4 1407 ± 4.1 1407 ± 2.1

193.8 ± 3.4 206.9 ± 1.2 201.7 ± 3.2

28.7 ± 0.2 24.7 ± 0.4 21.6 ± 0.5

3

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Fig. 3. Example microstructures of a vertically-built specimen: X-Y (a) and Z (b) sections from interior of specimen, X-Y section at edge of section (c) and higher magnification of Z section (d).

test conditions, and while in practice the notion of an endurance limit or design limit may be used, for example via the Goodman diagram [33], it does not represent a true endurance limit for this alloy [34].

samples that did not fail at 482 MPa maximum stress and R = 0.1 were subsequently tested at Smax 552 MPa and R = 0.1 and failed after 519,552 and 713,618 cycles, respectively. The goal was to test the specimens under similar loading conditions that would lead to failure and expose the fatigue-limiting defect. These two results are slightly higher than the corresponding values for vertical specimens with asbuilt surfaces based on the S-N curve in Fig. 5. They fall within or just below the range for the family of samples tested at 482 MPa in Fig. 8 and Table 3. The fatigue limit (at 107 cycles) for Smax 482 MPa and R = 0.1 was estimated from the S-N curve (Fig. 5) to be 450 MPa (Table 1). Testing at a slightly higher maximum stress was intended to better define the variation in fatigue life near the conditions associated with test termination at 107 cycles and constrain the fatigue strength at this lifetime. The results show the challenge in determining a practical fatigue limit for an S-N curve that exhibits a transition from fatigue life controlled by fatigue crack growth to crack initiation control. These tests were performed at Smax less than 10% higher than the estimated value in Table 2

3.3. Fatigue test results: fatigue life variation at discrete load conditions Based on the results for vertical specimens with as-built surfaces, additional tests were performed with loads intended to target approximately 106 to 2·106 cycles to failure. As can be seen in Fig. 5, there is a very narrow range in applied cyclic stress that encompassed failures from 106 cycles up to tests terminated at 107 cycles. Results for multiple samples run at either Smax 482 MPa at R = 0.1 or 345 MPa at R = −1 are presented as cumulative probability plots in Fig. 8. Thirteen tests were run at the former condition, with two reaching 107 cycles without failure and are censored from this plot. Eleven tests were run at R = −1 and all tests resulted in failure. Results of these tests are also presented in Table 3. Both the mean of the cycles to failure, and the mean of the logarithms of cycles expressed as Nf are included. The two

Fig. 4. Comparison of microstructure of vertical specimen (a) and angled specimen (b) adjacent to respective fracture surfaces. Arrows show build direction for each case. 4

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Fig. 7. Comparison of fatigue results for angled and vertical specimens, all with as-built surfaces.

Fig. 5. Fatigue results for vertical specimens with as-built surfaces.

Table 2 Estimated fatigue limit (at 107 cycles) of various test conditions in this investigation along with reference values for wrought material and LPBF from other sources.

Fig. 6. Fatigue results for samples with machined surfaces. Vertical specimens with as-built surfaces (ABS) at R = 0.1 are also plotted as in Fig. 5. Values from MIL-HDBK-5/MMPDS [21] for wrought materials are shown for comparison and reference. MMPDS values were derived from bar or plate stock and tested in the longitudinal direction with a gauge diameter of 5.08 or 6.35 mm.

Specimen Type

Print Orientation

Surface Condition

Stress Ratio

Estimated Fatigue Limit (MPa)

Reference

Uniform

Vertical

As-Built

−1 0.1 0.5

Fig. 5 Fig. 5

Uniform Hourglass Hourglass Uniform

Vertical Vertical Vertical Horizontal

Machined As-Built As-Built Machined

Uniform

Angled

As-Built

Wrought Bar

N/A

Machined

0.1 −1 0.1 −1 0.1 0.5 −1 0.1 0.5 −1

275–300 450 Insufficient Data 625 300 450 450 625 950 350 450–490 550–575 450

Uniform

Vertical Vertical

0.1 0.5 0.1 0.1

700 900 275–300 700

0.1

700

Horizontal

As-Built Low Stress Ground Low Stress Ground

Fig. Fig. Fig. Fig. Fig. Fig. Fig.

5 5 5 6 6 6 7

MMPDS [21]

Wells [26]

positions in the horizontal plane of the printer. Positions 45, 135, 225 and 315° are the bisectors of the X and Y axes in the printer’s frame of reference. In build plate layouts shown in Fig. 2, the front of each build plate is equivalent to the 180° position and the right-hand side is 90°. In contrast, vertical specimens that were machined, while relatively fewer in number (n = 6), show a wider distribution of fracture initiation position, encompassing five different locations among the six samples. The Concept Laser M2 equipment used to make these samples was operated so that a 90° offset between subsequent layers was used with an island scanning approach, with raster directions coincident with the x-y axis bisection line. The fatigue crack initiation is strongly favored to be at an azimuthal position consistent with the edges of these islands. A common fatigue crack initiation site feature is shown in Fig. 10, highlighting a typical characteristic of numerous specimen fracture

based on Fig. 5. The range of cycles to failure for the eleven samples that failed and the run-out achieved for two samples suggest that the value of 450 MPa is a conservative estimate of fatigue limit based on testing at a maximum stress more than 30 MPa above the estimated fatigue limit. 3.4. Fatigue crack origination features and locations Identification of fracture origins in these samples has led to the apparently new observation that the azimuthal location of fatigue crack initiation within round specimens tested with as-built surfaces with respect to the build area of the printer was not randomly distributed. A histogram (Fig. 9) shows that the position of estimated crack initiation location (to the nearest 22.5°) is heavily favored towards off-axis 5

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concluded that in using contour scans to make the fatigue specimens, the azimuthal position of the start and end of the contours on the circumference of the specimens led to preferred locations of crack initiation. 4. Discussion 4.1. Influence of test variables on fatigue behavior Analysis of the fatigue test data is made using two approaches, First, for samples with finite Nf, the S-N curves in Figs. 5–7 are modeled using the following form of Basquin’s equation:

Smax = A1 N fA2

(1)

The logarithm of this empirical relationship takes a linear form and can be applied to tests where run-out did not occur, i.e., tests that were suspended at 107 cycles are not included. Linear regression of the various data sets was performed, and values of coefficient of determination R2 and exponent A2 are shown in Table 4 from which pair-wise comparison of similar test specimen conditions (i.e., stress ratio and surface condition) is possible. Data sets for horizontal specimens are not included in Table 4 for R = 0.5 and R = −1 because no other specimen geometry with the same surface condition was tested, but the values of the coefficient of determination (R2) were 0.06 and 0.65, respectively. For the case of R = 0.5 this indicates the test data were not fit by linear regression of Eq. (1) (see Table 4). Comparison is made by noting that the ratio of the slope A2 and the standard error of its estimate se for a given data set are fit by the t distribution, and a test for the hypothesis that the slopes of two such data sets A2,1 and A2,2 with standard errors se,1 and se,2, respectively, are not significantly different is given by

Fig. 8. Failure probability based on test results at two loading conditions. Suspended tests (at 107 cycles) are not plotted.

surfaces examined using scanning electron microscopy. These nearly circular features are approximately 25 μm radius and are found adjacent to but within the as-built specimen surface. An example of two similarly-sized features adjacent to each other on the same fracture surface is shown in Fig. 11. In this specimen, no similar features were noted on the opposite fracture surface of the broken specimen. These features were not seen in all fracture surfaces that were examined and were often seen on only one surface of a fractured specimen but not the other. Aside from adjacent examples such as in Fig. 11, these features were only found at the crack origin within the thickness of the outer contour scan at the edge of the specimen. Taken individually, these features are similar in shape and size to other examples of features observed on fracture surfaces of LPBF test specimens as depicted for precipitation hardened stainless steel [35,36], aluminum alloy [37], or Ti-6Al-4V [38]. The current results are different from these examples in being singular or paired features adjacent to the as-built surface as illustrated in Figs. 10 and 11, and not distributed throughout the material. This condition is thus not identical to a similar feature shown adjacent to the specimen surface for 17-4 PH stainless steel, which was for a machined specimen [36]. While the use of contour scans is intended to improve surface roughness, especially when using island scanning as was done here, control of the start and end position of the contour scan and layout of the islands was not controlled for these specimens. The contours are circular for round specimens and constitute the outer surface for specimens tested with as-built surfaces. These are printed after the interior of the specimens at each layer, so the influence of raster direction for the interior of the specimen would seem to be less important and may be coincidental to the preferred crack initiation location. Therefore, it is

t=

A2,1

A2,2

se2,1 + se2,2

(2)

A level of significance of 0.05 was used for statistical tests based on Eq. (2). The other estimator in Eq. (1), the y-intercept or A1, is not appropriate to this analysis. This value represents Nf = 1, which is equivalent to the tensile strength, and is thus not a reasonable continuation of the data described by Eq. (1) for a high-cycle fatigue test predicated on elastic regime loading in each cycle. A significant difference between data sets that would meaningfully affect the value of A1 would be a systematic difference in Nf at a given loading condition, which by inspection of Figs. 5–7 does not occur. Basquin’s equation is only applicable to samples that fail, so the second approach to analyzing fatigue test data is the fatigue limit at 107 cycles, which is estimated for various cases and tabulated in Table 2. It is emphasized that these are estimates, because the scatter in fatigue life at loading conditions near the fatigue limit is considerable and may exceed one full log cycle. This is also seen for wrought material, as shown in Fig. 6. In two cases where the data could not be fit by a linear regression, namely hourglass specimens tested at R = −1 and horizontal specimens tested at R = 0.5, low values of R2 were due to insufficient test data at higher loads and correspondingly lower Nf. The data that was collected at higher Nf allowed for an estimate of fatigue limit.

Table 3 Summary of results for multiple specimens tested at one of two loading conditions. Test Condition (Smax/ R)

Number of tests

Number suspended at 10 M cycles

Minimum cycles to failure

Maximum cycles to failure (excludes run out)

Mean cycles to failure

10^(Mean log(Nf))

482 MPa/0.1 345 MPa/-1

13 11

2 0

569,740 499,718

1,649,744 2,244,700

868,393 1,233,796

833,022 1,129,263

6

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Fig. 9. Histogram of fracture initiation locations with respect to LPBF equipment frame of reference per the scheme in the inset figure.

4.1.1. Specimen geometry and orientation The only viable statistical comparison that can be made for differences in specimen geometry (uniform versus hourglass profile) is for the R = 0.1 condition tested with as-built surfaces. As shown in Table 4, the test results for hourglass specimens at R = −1 cannot be accurately modeled using Eq. (1). The relatively large scatter in the hourglass specimens tested at R = −1 is due to all of the tests’ being conducted close to the fatigue limit at 107 cycles (estimated to be 300 MPa). At R = 0.1, a statistical comparison can be made and there is no significant difference between uniform and hourglass specimen design at this stress ratio. In addition, for both stress ratios the estimated fatigue limit at 107 cycles is approximately the same. On this basis, it is concluded that for round specimens the fatigue behavior does not depend on specimen geometry. The uniform gauge specimens contain two interfaces between the gauge section and the radiused transition, and the hourglass specimens have a single plane of highest section stress. The similarity between the two indicates that there is not an unique population of life-controlling features associated with either geometrical features after full HIP and heat treatment.

For horizontally built specimens, the only comparison is made to machined vertical specimens at R = 0.1, which shows no significant difference based on Eq. (1) data or in fatigue limit, which is estimated to be 625 MPa for both cases. Comparison between vertical and angled specimens can be made at all three stress ratios with as-built surfaces. There is not a significant difference for specimens that failed at any of the three stress ratios. The estimated fatigue limit of the angled specimens is slightly higher at R = −1 and R = 0.1, but no comparison can be made at R = 0.5 given the absence of run-out for vertical specimens. Given the approximate nature of the fatigue limit additional testing at the estimated fatigue limit would be needed to confirm whether this difference is significant. 4.1.2. Surface condition The influence of surface condition is made by comparing vertical specimens at R = 0.1 with either as-built or machined surfaces. In contrast to specimen geometry or orientation, machined and as-built surfaces is the only direct comparison of Eq. (1) that resulted in a statistically significant difference. In addition, the difference in estimated

Fig. 10. Inferred failure site on opposite surfaces of a single failed specimen. This sample was initally tested at R = 0.1 and 482 MPa maximum stress and reached 107 cycles without failure, and then was retested at R = 0.1 and 552 MPa maximum stress to cause failure at 519,552 cycles. 7

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Fig. 11. Fatigue crack initiation site of a sample tested at R = −1 and 345 MPa maximum stress with Nf ~ 700 K. Table 4 Coefficients of Eq. (1) for data sets excluding run-out tests. Specimen Type

Print Orientation

Surface Condition

Stress Ratio

n (failed tests only)

R2

A2

Uniform

Vertical

As-Built

Uniform Hourglass Hourglass Uniform Uniform

Vertical Vertical Vertical Horizontal Angled

Machined As-Built As-Built Machined As-Built

−1 0.1 0.5 0.1 −1 0.1 0.1 −1 0.1 0.5

8 8 8 6 5 7 9 9 10 7

0.83 0.90 0.99 0.90 0.04 0.84 0.55 0.69 0.55 0.97

−4.4 −5.0 −4.0 −9.2 −1.2 −6.7 −6.2 −6.0 −5.5 −4.5

0.1 0.1

19 8

0.89 0.52

−3.5 −6.5

0.1

8

0.78

−9.1

Results below from Ref. [26] Uniform Vertical Vertical Horizontal

As-Built Low Stress Ground Low Stress Ground

Fig. 12. Comparison of fatigue test results from the current investigation with those from Wells [26]. Data for Vertical ABS samples noted with (2) are identical to those in Fig. 8, with two tests at R = 0.1 and 482 MPa maximum stress that reached run-out included to extend full range of results.

maximum post-build thermal exposure was not likely to have converted the as-built microstructure to the generally equiaxed, anisotropic example shown in Fig. 3. One study that tested specimens with as-built surfaces after solution treatment and aging tested at a single loading condition (900 MPa maximum stress, R = 0.1), with failures occurring from just under 20 K to approximately 50 K cycles [17]. At the high end of this range in Nf there is potential overlap with results for vertical specimens in Fig. 5. Another study also used solution treatment and aging and developed S-N curves at R = −1 for machined horizontally oriented specimens [18]. The fatigue limit for this study was no more than 300 MPa, which is far below the value of 450 MPa for horizontal machined specimens in Table 1. One source for fatigue data that was both HIP’ed and heat treated was published by NASA [26], which are compared to the present results in Fig. 12. Published data is for both low stress ground (LSG) and asbuilt surfaces. Regression fits based on Basquin’s equation for the published data are also included in Table 4. Comparison of the similar cases based on Eq. (2) indicates that for specimens that failed, the machined horizontal and vertical in the present case and the LSG horizontal and vertical that were already published are not different at a 0.05 level of significance. The fatigue limit of machined samples for the previously published data is estimated to be 75 MPa greater than the present materials, which is similar to the difference for wrought material. This difference is more likely to be due to differences in specimen preparation than intrinsic differences in material. When specimens with as-built surfaces are compared, however, differences based on Basquin’s equation are statistically significant for the case of vertical specimens at R = 0.1. This is not readily seen in the S-N curves in Fig. 12, where up to Nf ~ 500,000 and maximum stress of 500 MPa there is not a large difference. The most notable differences arise beyond this point in the S-N curve, at lower loads and longer cycles to failure. In addition, the relative differences in estimated fatigue limit is reversed, with the present material exceeding the published material by approximately 150 MPa. The debit in fatigue life relative to a machined surface is approximately 28% for the present material but more than 50% for the previously published material. Also plotted in Fig. 12 are fatigue test results at Smax 482 MPa R = 0.1 and 345 MPa R = −1, which are taken from Fig. 8 with the

fatigue limit is 175 MPa, which represents a debit due to as-built surface of more than 25%. By comparison, differences in the fatigue limit for angled and vertical specimens were approximately 10%. 4.1.3. Comparison to wrought material and published LPBF data The fatigue limit at 107 cycles for wrought material is estimated to be 450, 700 and 900 MPa at stress ratios of −1, 0.1 and 0.5, respectively [21]. For horizontal specimens with machined surfaces, the corresponding values are estimated as 450, 625 and 950 MPa, respectively; for vertical LPBF specimens with machined surfaces the value at R = 0.1 was 625 MPa. The similarity between LPBF 718 with machined surfaces and wrought material was previously shown for a full S-N curve for notched specimens (Kt = 3) [27], with a decrease in fatigue limit of approximately 40% due to as-built surfaces. In the present case, the debit in fatigue life for as-built surfaces compared to machined surfaces for vertical LPBF specimens at R = 0.1 is 28% for the uniform gauge specimens. The estimates in Table 2 for as-built surfaces of vertical and angled specimens are 30 to 40% lower than the corresponding value for wrought. Given the results for machined specimens, this difference is primarily due to surface condition in the as-built specimens. The number of available published studies for high-cycle fatigue of laser powder bed fusion of alloy 718 that received similar post-build thermal treatment (consisting of HIP and solution treatment and aging following AMS standards) is limited. There are several recent studies of uniaxial fatigue testing that did not use HIP’ed material and thus the 8

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addition of two run-out results at the former test condition. The mean failure life at a maximum load per cycle of 345 MPa for fully reversed loading (R = −1) was 1.12 M cycles, but the upper range of this data overlaps with previously published data tested at R = 0.1. The fatigue limits for these two cases (Table 2) are similar. Given this similarity, the large difference for specimens with as-built surfaces is inferred to mean that fatigue crack initiation sites are different. This is traceable to the original printing conditions and would not have been influenced by subsequent thermal treatments. 4.2. Influence of surface roughness As-built surfaces in LPBF materials give rise to lower fatigue lives and fatigue limits than machined counterparts. This may be loosely ascribed to surface roughness, but it has been asserted that the value of conventionally measured surface roughness is not directly correlated with fatigue behavior [39]. Rather, it is features that intrude into the section under test that control crack initiation. Yadollahi et al. [25] explicitly recognized this in using mean valley depth from surface profile measurements as a minimum surface feature size (40 μm) and maximum valley depth as a worst-case or lower-bound condition (110 μm). The crack initiation sites in the present work (such as Figs. 10, 11 and 13) are slightly smaller than 40 μm, and just as important, may be considered as near-surface lack-of-fusion or porosity defects associated with use of contour scans and are not detectable in surface profile measurements. This hints at the importance of understanding fatigue-limiting features based on their presentation on fracture surfaces and not only from surface roughness [40,41]. This is illustrated in comparison of fracture origins in specimens with as-built surfaces built at an angle or vertically and were each tested at R = 0.5 (Fig. 13). The angled specimen was tested at a maximum stress of 586 MPa and failed at 1.41∙106 cycles, while the vertical (depicted at higher magnification in Fig. 14) was tested at 552 MPa and failed at 1.40∙106 cycles. In comparing the fracture surfaces, however, it is apparent that the vertical specimen presents a relatively smoother surface contour, as is typical in comparison of vertical and angled downskin surfaces in laser powder-bed fusion [42]. Part of this is due to higher density of adhered powder particles on the angled surface, but this also contains several locations where an intruding surface defect is present, while none are seen on the vertical specimen. Nevertheless, the angled specimen failed at approximately the same number of cycles. Taken from the approximate extent of the net section, both the rough downskin surface in the angled specimen and the contour-scan related features in the vertical specimen penetrate into the net section by 50–100 μm, so a typical surface profile measurement such as Ra that incorporates the unmelted powder would be as inaccurate in the angled case as Rv would be in the vertical case where the crack-initiation

Fig. 14. Fatigue crack initiation area with adjacent near-surface round features in a vertical specimen that was tested at R = 0.5, 552 MPa maximum stress with Nf ~ 1.4 M cycles.

controlling feature is a subsurface feature surrounded by solidified material. Thus, attempts at fatigue life prediction would be more accurately bounded by feature dimensions taken from examination of fracture surfaces, not surface profile measurements. 4.3. Feature size control of fatigue crack initiation The small differences in fatigue limit between machined LPBF and wrought 718 and the significant differences (approximately 175 MPa) for LPBF 718 with as-built surfaces indicate that the difference between the as-built surface results for the present materials and Reference [26] can be attributed to differences in surface condition. This raises the question of what specifically about the as-built surface controls fatigue crack initiation and overall fatigue life. This question has been typically approached based on the relative sizes of defects present in the material. With reliable data for fatigue crack growth rates, S-N type of behavior has been predicted from a fracture mechanics approach modified to account for plasticity ahead of the crack tip and the possibility of crack closure during unloading from maximum stress [43]. This modeling approach has been applied to alloys fabricated by additive manufacturing with reasonable accuracy [44,45], and was used by Yadollahi et al. [25] to analyze alloy 718 fabricated by laser powder-bed fusion [26,46]. A qualitative assessment of this analysis showed that the predictions of fatigue life were less successful for test data for as-built surfaces than machined surfaces. The authors concluded that the model was conservative for material with an as-built surface and conjectured

Fig. 13. Comparison of fatigue crack origin locations in angled (left) and vertical (right) specimens that were tested at R = 0.5 and failed at 1.4 M cycles. The maximum stress in the angled specimen was 586 MPa and in the vertical it was 552 MPa. 9

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that crack initiation mechanisms which correlated with stress or multiple initiation sites might be responsible for the difference in the model accuracy for LSG and as-built surfaces. For the case of coalescence of fatigue cracks initiating from multiple locations, examples for laser powder-bed fusion of the precipitation hardened stainless steel 17-4 have been reported for cases of loadcontrolled [36] or strain-controlled [47] fatigue, but these were for materials that had not been hot isotatically pressed, and retained asbuilt macrostructural features such as melt-pool boundaries. The multiple initiation sites favored unclosed porosity. The current results indicate that a single initiation site dominates for round Inconel 718 specimens that have been recrystallized through HIP, which is consistent with results for traditional powder metallurgy 718 [48]. As for the possibility of stress-dependent crack initiation mechanisms, a more straightforward explanation is that different surface features are responsible for differences in fatigue life as Smax decreases. In considering the results from Fig. 12, data for two sources of LPBF 718 alloy were similar for machined surfaces, with differences only emerging in the case of as-built surfaces. This suggests that a method for estimating the influence of surface features on fatigue crack origin could be used to explain such differences. The fatigue limits in Table 2 for materials with as-built surfaces are used to estimate a threshold stress intensity associated with this surface condition. This approach is predicated on an assumption that the estimated fatigue limit can be treated as a sub-threshold condition with no fatigue crack growth having occurred at 107 cycles. Some measure of validation for this assumption is based on the results from two specimens that were tested at R = 0.1 and Smax 552 MPa after reaching run out at R = 0.1 and Smax 483 MPa. The subsequent testing at slightly higher maximum load resulted in Nf that was greater than the S-N curve would have predicted, which in turn means that pre-existing crack initiation is less likely to have occurred prior to run out in the first test. Estimates for threshold stress intensity range are based two published methods for estimating KI for the case of a surface crack in a cylindrical rod under remote tensile stress. Raju and Newman [49] used finite element simulations to evaluate the expression

KI = S

a F Q

this model utilized a simplified crack geometry in which the free surface of the crack intersected the cylinder surface at a right angle. Eqs. (3) and (4) were used to approximate the ΔK associated with the fatigue limits for as-built surfaces in Table 2. Crack depths were analyzed as either 50 or 100 μm, consistent with features seen in Figs. 10 and 11. For the case of a single pore as an origination site a = 50 µm was used. A fracture surface containing two adjacent contour scan features is shown in a vertical specimen in Fig. 11. For this case, a is closer to 100 µm and the two features are separated by closer to 200 μm, which in this case is equivalent to 2c and a/c = 0.5. Other relevant constants necessary to solve for K are the specimen diameter (6.35 mm), while the maximum and minimum stress values are based on experimental conditions. Other details of Eqs. (3) and (4) are available in the respective references, but no other experimental values are required. Estimates of threshold ΔK in Table 5 are generally in the range of 2–6 MPa √m. For comparison, a reference value of ΔKth for wrought Inconel 718 from MMPDS-12 is around 7–10 MPa √m for R = 0.05 [21]. Yamada and Newman estimated a value of ΔKeff,t of 2.7–3.1 MPa √m at R = 0.7 for an alloy 718 forging [51], where the quantity ΔKeff,t incorporates crack closure and assumes a lowering of the effective stress intensity range [52] by the need for a crack opening force that is larger than the minimum stress associated with Kmin [43,52,53], although the concept of crack closure has been the matter of some dispute [54–56]. The modification of ΔKt to determine ΔKeff,t is based on fitting of da/dN curves collected at different R values and it has been noted that the crack-opening stress intensity thus derived may be more dependent on the method used to condense multiple da/dN curves into a single curve and less influenced by the material itself [57]. In the case of LPBF materials with as-built surfaces, a population of surface or near-surface defects that influence the high-cycle fatigue behavior would not be a factor in fatigue crack growth testing that used machined specimens with pre-cracks introduced under cyclic loads. The estimated value of threshold ΔK suggested here for as-built surfaces is one proposed way to reckon with the uncertainty regarding surface initiation of fatigue cracks that avoids the assumptions of curve fitting in ΔKt,eff and removal of the as-built surface in ΔKth and fatigue-crack growth rate testing more generally.

(3)

for the geometry correction factor F. Other terms include remote tensile stress S, crack shape factor Q, and crack depth a. F was evaluated for various conditions of a/c where c is the crack half arc-length at the surface of the cylinder, a/D where D is the cylinder diameter, and whether the expression was evaluated at the maximum depth of the crack or where it intersected the free surface. Forman and Shivakumar [50] used a similar approach and formulation expressed as

KI =

0F ( 0)

5. Conclusions Inconel 718 made by laser powder-bed fusion and then recrystallized by hot isostatic pressing and solution treated and aged was subjected to extensive uniaxial high-cycle fatigue testing. Two new observations emerged for specimens tested with as-built surfaces concerning the relationships between failure locations and the powder-bed fusion process. These are attributed to the use of the combination of island scanning and contour scans. First, there is an apparent bias in the failure location in the frame of reference of the powder bed printer due because contour scans do not start and finish at random locations and interior island scans are aligned with off-axis directions in the printer’s frame of reference. Second, the fatigue crack initiation can consistently

(4)

a

where subscript 0 signifies tensile stress, σ is remote stress, and F(λ) is a so-called magnification factor that was a function of a/D. The main assumption in this method, in contrast to Raju and Newman, was that Table 5 Estimates of threshold ΔK of as-built surfaces based on Eqs. (3) and (4) Max/Min Stress (MPa)

ΔK at Fatigue Limit: Eq. (3)

ΔK at Fatigue Limit: Eq. (4)

Maximum crack depth a/c = 1

310/−310 450/45 550/275

Free Surface a/c = 0.6

a/c = 1

a/c = 1

a/c = 0.6

a = 50 µm

a = 100 µm

a = 50 µm

a = 100 µm

a = 50 µm

a = 100 µm

a = 50 µm

a = 100 µm

a = 50 µm

a = 100 µm

a = 50 µm

a = 100 µm

4.2 2.7 1.9

5.9 3.8 2.6

5.6 3.7 2.5

7.9 5.2 3.5

4.8 3.1 2.1

6.7 4.4 3.0

4.7 3.1 2.1

6.7 4.4 3.0

4.3 2.8 1.9

6.1 3.9 2.7

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be traced to small, circular features lying within the width of the contour scans. These features are generally singular in nature or closely spaced and are not found away from the fatigue crack growth initiation site. S-N curves were generated over a range of stress ratios, specimen orientations and surface conditions. Comparison of these curves leads to the conclusion that for a given combination of stress ratio and surface condition, there is no significant difference between the S-N curves. Vertical and angled specimens with as-built surfaces were also not significantly different. Horizontal specimens for these specimen geometries cannot be made without build supports, so testing horizontal specimens with as-built surfaces is not possible. Nevertheless, horizontal and vertical specimens with machined surfaces were not significantly different, although this comparison was made at a single stress ratio (R = 0.1). Multiple vertical samples with as-built surfaces were tested at a single loading condition (at either R = −1 or R = 0.1) and showed that the range of cycles to failure in a loading regime near a transition from fatigue life controlled by fatigue crack growth to control by fatigue crack initiation is difficult to pinpoint based on S-N curves. Comparisons to previously published data for LPBF 718 alloy given similar post-build thermal treatments showed no significant differences for machined specimens, but significant differences for vertical specimens with as-built surfaces tested at R = 0.1. This result highlights the importance of surface characteristics in determining fatigue behavior. Estimated fatigue limits for the case of as-built surface conditions at R = −1, 0.1 and 0.5 were used to estimate threshold values of stress intensity range ΔK that are representative of the as-built surface condition. This value is not equivalent to ΔKth derived from fatigue crack growth testing, where testing with a machined or pre-cracked specimen would undermine the ability to evaluate the as-built surface. Values of the as-built surface ΔK across the range of stress ratios were primarily in the range of 2–6 MPa √m. These values are related to surface conditions, especially the size of features where fatigue cracks initiate, so they are not necessarily representative of LPBF 718 alloy in general. In addition, the fatigue limits from which the threshold ΔK was measured are based on material that was HIP’ed and solution treated and aged, and are likewise not likely applicable to versions of the alloy that are tested in a different microstructural condition. Nevertheless, it provides a basis for interpreting high-cycle fatigue results of LPBF 718 with asbuilt surfaces.

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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. Acknowledgements This work was supported in part by The Aerospace Corporation’s Independent Research and Development program. The manuscript has been improved by comments from reviewers. All trade names, trademarks, and service marks are the property of their respective owners. Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.ijfatigue.2019.105392. References [1] Gorelik M. Additive manufacturing in the context of structural integrity. Int J Fatigue 2017;94:168–77. [2] Daniewicz SR, Shamsaei N. An introduction to the fatigue and fracture behavior of additive manufactured parts. Int J Fatigue 2017;94:167. [3] Li P, Warner DH, Fatemi A, Phan N. Critical assessment of fatigue performance of additively manufactured Ti-6Al-4V and perspective for future research. Int J Fatigue

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