Fatigue strength improvement of additively manufactured 316L stainless steel with high porosity through preloading

This work investigates the influence of a single tensile preload, applied prior to fatigue testing, on the fatigue strength of 316L stainless steel parts manufactured using laser-based powder bed fusion (PBF-LB) with a porosity of up to 4 %. The specimens were produced in both the horizontal and vertical build directions and were optionally preloaded to 85 % and 110 % of the yield strength before conducting the fatigue tests. The results indicate a clear tendency of improved fatigue life and fatigue limit with increasing overload in both cases. The fatigue limits increased by 25.8 % and 24.6 % for the horizontally and vertically built specimens, respectively. Extensive modelling and experiments confirmed that there was no significant alteration in the shape and size of the porosity before and after preloading. Therefore, the observed enhancement in fatigue performance was primarily attributed to the imposed local compressive residual stresses around the defects.


Introduction
Additive manufacturing (AM) is a rapidly emerging manufacturing technology wherein a component is produced layer by layer based on a three-dimensional CAD model.Therefore, AM possesses the potential to revolutionize the landscapes of the manufacturing industry and logistics.It enables on-demand production of parts and the creation of complex geometries, including topologically optimized structures that are difficult or even impossible to manufacture using traditional subtractive techniques.Consequently, AM offers the opportunity to reduce costs, energy consumption, carbon footprint and material waste through design optimization [1,2].
Among the AM processes, powder bed fusion (PBF) is widely utilized for manufacturing metallic materials [3].Specifically, laser-based powder bed fusion (PBF-LB) is the most established and commonly used method.This process operates at a relatively low powder bed temperature, typically ranging from 100 to 400 • C [4,5].However, where the laser is irradiated, a high and focused energy is locally applied, heating and melting the metal powder.This creates a metal melt pool that can reach temperatures as high as 2500-3500 • C [2,[4][5][6].
Within a single layer, the laser beam continuously moves to different locations, and the molten regions solidify rapidly at a typical rate in the range of 10 3 -10 6 • C/s [2,4,5,7].After melting, the entire layer undergoes further solidification, while a new layer of powder is distributed on top of it.This newly deposited layer is then melted and solidified following the same pattern.Additionally, the actively melted layer can transfer heat and fuse together with the preceding layer, leading to shrinkage during solidification.This process, combined with shrinkage, contributes to uneven surface/volume temperature and a significant temperature gradient.The complex thermal history in PBF-LB can result in substantial residual stresses [6].
In addition to residual stress, as-built PBF-LB parts may also contain various defects, including a rough surface, porosity and lack of fusion (LOF) defects.The rough surface is mainly caused by the layer-wise staircase effect, laser tracks and lateral sintering of the powder [7].These factors contribute to irregular surface features that can act as stress concentrators, thereby reducing fatigue strength and life.Porosities, on the other hand, result from entrapped gas and are generally spherical and smaller in size [6,8,9].On contrast, LOF defects can reach a much larger size that is often several times larger than gas pores.They are formed due to insufficient laser energy caused by improper processing parameters.These defects typically contain unmolten powder particles and exhibit irregular shapes with sharp corners.As a result, they frequently act as sites for initiating fatigue cracks due to local stress concentrations around the defects [4,5].LOF defects are typically affected by PBF-LB parameters such as laser powder, scanning speed, hatch spacing, powder layer thickness, etc. [6].Nevertheless, it is interesting to note that the effect of the inter-layer time interval during manufacturing could be negligible on the mechanical properties of stainless steel PBF-LB fabricated specimens.This is attributed to the small thickness of the powder layer and the fact that the component is surrounded by powder which serves as an insulator to the heat transfer [10][11][12].
The improvement of the fatigue life of PBF-LB made components has been the subject of considerable research.Jambor et al. [13] found that components made using PBF-LB with 304L stainless steel have lower resistance to fatigue crack propagation compared to its traditionally manufactured counterparts.This was attributed to the reduced plasticity-and roughness-induced crack closure due to the dislocation cellsubstructure undergoing phase transformation.Man et al. [14] observed deformation induced martensite during the fatigue process of 316L stainless steel.Wang et al. [15] reported inferior fatigue performance in PBF-LB made 316L specimens compared to rolled 316L, which was attributed to the presence of defects that promoted microcrack initiation and accelerated crack propagation, resulting in brittle failure modes without plastic deformation.In contrast, rolled 316L exhibited ductile fracture with striation patterns.Tomaszewski [16] presented a modelling approach to analyse the size effects in PBF-LB made 316L stainless steel.While there are challenges, several research articles highlight the advantages of PBF-LB made stainless steel over its wrought counterpart.For example, PBF-LB 304L exhibits special non-equilibrium structures such as cellular structures, high-density dislocations and nanoparticles, enhancing its mechanical properties and fatigue crack nucleation resistance [4,5,[17][18][19].Additionally, Waqar et al. [20] and Serrano-Munoz et al. [21] demonstrated that preheating and in-situ rescanning techniques in PBF-LB can significantly reduce residual stresses, offering an alternative to time-consuming post-processing techniques.
Several studies [22][23][24][25][26] have demonstrated the beneficial effect of preloaded or prestrained specimens on the fatigue life of conventionally manufactured materials.Preloading induces compressive residual stresses on the surface and blunts sharp edges on the defects.However, the application of static preloading as a fatigue life enhancer in AM components has scarcely been investigated.Therefore, this study aims to fill this research gap by investigating the effect of preloading, prior to the functional operation of the part, on the fatigue behavior of PBF-LB specimens, particularly in the presence of a significant level of porosity.This is accomplished by examining the alterations in the fatigue behavior of 316L PBF-LB parts with a moderate level of porosity, in response to a single cycle of tensile preload before a standard fatigue test.Both preloading below and above the material yield strength are investigated.An in-depth experimental investigation of defect shape before and after preload, fracture surface analysis as well as the alteration of the residual stress state due to the preloading is performed.This is followed by a numerical analysis, highlighting the interplay between preloading-induced residual stress and initial residual stress from the PBF-LB manufacturing.

Manufacturing
The commercial 316L stainless steel powder (Renishaw, UK) was employed in this study.The powder used was gas atomized and had a spherical shape in the range of 15-45 µm with some instances of attached satellites (i.e., smaller particles attached to the main spherical particles), as depicted in Fig. 1a.The PBF-LB process was carried out using the AM400 Renishaw (Renishaw, UK) machine to manufacture cuboid blocks, as shown in Fig. 1b.Subsequently, these blocks were cut into test specimens.These cubic blocks were built directly on top of a stainless steel plate (200 × 200 × 10 mm 3 ).Both vertical samples (V1-V9 in Fig. 1b) and horizontal samples (H1-H9 in Fig. 1b) were produced in the same batch, with dimensions of 20 × 30 × 110 mm 3 .The inlet flow direction can be observed in Fig. 1b, while the stainless steel powder was consistently recoated in the perpendicular direction, see Fig. 1b.To prevent chemical oxidation, an inert atmosphere was created using Argon gas throughout the process.The cuboids were manufactured using the process parameters shown in Table 1, without preheating.The gas velocity was reduced to 1.13 m/s and the layer thickness was increased to 50 µm to obtain an increased porosity in the blocks [27].A meander laser scanning strategy using 67 • rotation between the layers was employed in the manufacturing.

Machining
The cubic blocks were detached from the plate and test specimens were extracted from the blocks using wire electrical discharge machining (EDM, Sodick VL400Q).Fig. 2 demonstrates the part being clamped on both ends during EDM cutting to prevent deformation due to the high residual stresses in the material.After releasing the clamps, the material remaining in the blocks underwent significant deformation owing to the residual stresses, as depicted in Fig. 2. Test specimens were extracted from the region where only hatching had been performed to ensure uniformity in their microstructure.Subsequently, they were sliced to a specified thickness of 2.5 mm.White Light Interferometry (WLI) microscopy was also used to measure the surface roughness after machining, with five measurements and a scanning length of 100 µm for each specimen.The surface roughness of the specimens after EDM was consistent for all specimens with a magnitude of 4-5 µm (Ra), which is similar to previously reported surface roughness for wire EDM [28].
Two types of testing samples were cut from the blocks: tensile specimens having straight central part (Fig. 3a) and fatigue specimens with a distinct waist (Fig. 3b).The tensile specimens were used to obtain monotonic stress-strain curves from uniaxial tensile tests while the fatigue specimens were used for the cyclic fatigue tests.Surface treatment was not applied to the specimens after EDM.

Mechanical testing
The uniaxial tensile tests and fatigue tests were carried out by use of a servo hydraulic testing machine (MTS), see Fig. 4a and b.The tensile tests were conducted with three specimens in both vertical and horizontal build directions, with a displacement-controlled rate of 0.015 mm/s.To account for any misalignments, two extensometers were mounted onto the gauge section.The fatigue tests were performed in force-control at an R-ratio of 0.1 and a frequency of 20 Hz.Despite the relatively high frequency level, deformation-induced heating can be neglected, as the specimens are solely exposed to pulsating cyclic loads.Consequently, the cyclic curves exhibit purely elastic behavior without any energy dissipation.Therefore, the consideration of deformationinduced heating can be disregarded [29].S-N curves, including fatigue limits computed using ISO 12107:2012 standard [30] and the staircase method [31], were obtained for specimens in their as-built condition (without preload) as well as specimens that were subjected to preloads 1 and 2 prior to cyclic fatigue loads, see Fig. 4c.This procedure was applied to both horizontally and vertically built specimens.Here, the yield strength, σ Y , is defined at 0.2 % plastic strain and the magnitudes of preload 1 and preload 2 are 0.85 σ Y and 1.1 σ Y , respectively.Additionally, the yield strength σ Y is different for the vertical and horizontal specimens.A preload was used instead of a prestrain since high cycle fatigue testing is typically conducted under force-control.This approach facilitated for fatigue tests at a higher frequency of 20 Hz, maintaining consistent preload conditions.Furthermore, the use of a preload rather than a prestrain made it easier to ensure an elastic preload 1 and a preload 2 exhibiting plastic behavior.A specimen is considered as a runout upon reaching two million cycles, and the test is then concluded.

Residual stress
X-ray diffraction (XRD) was used to measure the residual stress on the surface of the specimens, both before and after applying a preload.The measurements were conducted in accordance to standard [32].In total, three specimens were tested, including two horizontal and one vertical specimen.For each specimen, the stresses were measured in three different directions (as shown in Fig. 5): 0 • along the loading direction, 45 • from the loading direction and 90 • perpendicular to the loading direction.The measurements were conducted using a Bruker D8 Discover instrument with Cu K-alpha radiation and a 2 mm collimator.The stresses were calculated using the sin 2 (Ψ) method with the Bruker software Leptos.

Alteration of defect shape and stress state due to preloading
Archimedes' principle was used to measure the density and porosity of the sample blocks.Isopropyl alcohol served as the fluid for the density measurements, considering a theoretical density of 7.99 g/cm 3 for 316L stainless steel.In addition, a scanning electron microscope (SEM) was   utilized to measure the shape of 30 surface defects on both horizontal and vertical specimens before and after applying a preload.The mean change in roundness of the surface defects was calculated, where roundness is defined as where A and d are the projected area and the longest chord of the defect, respectively.The longest chord represents the diameter of a circle that encompasses the entire defect.The projected area and the longest chord of the defects were evaluated by use of the software ImageJ.The SEM images were imported into the software and both the area and the length were manually measured by precisely tracing the contours of the defects.Considering defects as crack initiation locations, a potential increase in roundness after preload would affect the crack geometry factor thus resulting in a longer fatigue life.The mean values of the change in roundness were thus experimentally quantified.
Furthermore, a change in the residual stress state at the specimen surface due to preloading affects the fatigue limit.This potential effect was estimated using the Smith-Watson-Topper (SWT) mean stress correction [33] given by σ e,eq = − 0.5 where σ m is the mean stress at the specimen surface during cyclic loading, σ e is the fatigue limit before mean stress correction and σ e,eq is the mean stress corrected fatigue limit.

Numerical simulation
To simulate the effect of preload on the local cyclic response of a surface defect, a 3D block was created in Comsol Multiphysics.The block featured a small elliptic cylinder hole on the surface, representing a LOF defect, see Fig. 6.The model represents one-eighth of the testing region in the fatigue specimen and the boundary conditions include three symmetry planes with prescribed displacements: u x = 0, u y = 0 and u z = 0.The dimensions of the 3D block are 5 mm × 3 mm × 1.25 mm and the semi-axes of the elliptic cylinder are 100 µm × 20 µm with a depth of 50 µm.The geometry and dimensions of the defect in the model are based on the SEM analysis performed on the largest defects on the specimen surface.The perpendicular orientation of the defect to the loading direction is chosen since it represents the most detrimental case in terms of stress concentrations and fatigue strength.
The initial residual stress state is based on the XRD measurements for the horizontal and vertical specimens with the value σ x on both surfaces.
Here, an assumption of − σ x is made for the residual stress in the middle of the specimen, where z = 0, with a bilinear stress distribution across the thickness of the specimen to maintain global equilibrium.Initial residual stresses in other directions are neglected.Rotations are not allowed on the loading surface which is expressed as r x = r y = r z = 0 and a boundary load is applied on the surface.The constitutive models describing the material response in the FE model are based on the isotropic and kinematic hardening models developed by Voce [34] and Armstrong-Frederick [35], respectively.The nonlinear isotropic hardening law is given by where σ Ys describes the expansion of the yield surface wherein σ Y0 is the initial size of the yield surface (cyclic yield strength) and σ sat is the saturation flow stress describing the final size of the yield surface.Here, β is a dimensionless saturation exponent describing the hardening rate while α is the accumulated plastic strain.It's important to note that σ Y0 in the Voce law differs from the monotonic yield strength from the tensile tests, as the former is considered a fitting parameter, whereas the latter is determined at a 0.2 % plastic strain.Generally, the cyclic yield strength tends to be lower than the monotonic yield strength, providing a more accurate depiction of the gradual transition from elastic to plastic behavior commonly observed in metal plasticity [36].The nonlinear kinematic hardening model proposed by Armstrong and Frederick is implemented in conjunction with the isotropic hardening law to achieve more flexibility for parameter identification.The back stress, σ b , in the kinematic hardening model defines the location of the center of the yield surface and has the evolution law  The kinematic hardening modulus is here given by C k while γ k is a nondimensional material-dependent parameter characterizing the nonlinear response.The evolutionary equation for the accumulated plastic strain is where εp is the plastic strain increment [37].The isotropic and kinematic hardening parameters were fitted by use of an inverse procedure where the global stress-strain response of the model was fitted to the tensile tests, see Fig. 7.The isotropic and kinematic hardening parameters are fitted to the monotonic stress response of the horizontal and vertical tensile tests up to preload 2 and preload 1, respectively.The Young's modulus values obtained from the tensile tests were utilized for both the horizontal and vertical specimens.Subsequent loading cycles, including unloading and reversed loading, are necessary to establish an accurate combined hardening model for the material.Since cyclic plasticity models for AM 316L are limited, the selection of hardening parameters were based on previous experience on modelling the elastoplastic response for a similar material [36].It is noted that, since the fatigue tests are performed with pulsating loading (R = 0.1), an elastic shakedown is expected and the material response in the cycles after the preload is thus elastic.

Porosity
The quantified porosity percentage for each as-built PBF-LB sample is shown in Fig. 8.No correlation was observed between porosity and the blocks' positioning concerning gas flow and recoating directions.The blocks exhibited a random porosity level ranging from 2 to 4 %.Moreover, porosity is uniformly distributed along the height of the blocks.This was confirmed through density measurements using Archimedes' principle, conducted on three samples obtained from the block residues.Consequently, the error bars depict only a slight variation in porosity among the blocks.These specimens were randomly selected for obtaining the S-N curves with and without preload.The high porosity is primarily attributed to the presence of a significant number of LOF defects in the blocks during the PBF-LB process.Gas pores are also present in the material, but they are considerably smaller in size, see Fig. 9. Since the LOF defects are larger and irregularly shaped, compared to the small and round gas pores, they have a more detrimental effect on the mechanical properties of the material.These large voids in the material possess sharp edges, resulting in high stress concentrations that enhance crack initiation when subjected to mechanical loading [38,39].

Mechanical testing
Fig. 10 demonstrates the average stress-strain curves after tensile test on vertical and horizontal specimens.As seen, the specimens with a vertical build direction are rather brittle compared to the relatively ductile horizontally built specimens.In addition, both the Young's  modulus and the yield strength are lower for the vertical specimens.The observed trend can be ascribed to the perpendicular orientation of the build layers in relation to the loading direction, along with the material's microstructure characterized by elongated grains aligned with the build direction.The S-N curves are shown in Fig. 11 where the red color is the fatigue performance without preload and blue and green color corresponds to preload 1 and preload 2, respectively.The mean curve is presented together with probability levels (5 % and 95 %) calculated according to the IIW Recommendations [40] using a two sided, 75 % confidence.The horizontal solid lines represent the experimental fatigue limits determined following the ISO 12107:2012 standard [30].The stress levels are determined based on the staircase method [31], see Fig. 12.The Basquin model [41] was then fitted to the data points above the fatigue limit to obtain the bilinear S-N curves.It is noted that the vertically built specimens were only subjected to preload 1 prior to the fatigue tests, since static fracture occurred upon applying preload 2. The preload magnitudes for the horizontal specimens were 408 MPa for preload 1 and 528 MPa for preload 2. Meanwhile, the vertical specimens had a preload magnitude of 340 MPa for preload 1.
A substantial improvement in fatigue performance from preloading is demonstrated in Fig. 11 for both the horizontally and the vertically built specimens.For the horizontal specimens, the fatigue limit increased from 93 MPa to 109 MPa for preload 1 and 117 MPa for preload 2, corresponding to a 17 % and 25 % improvement, respectively.For the vertical specimens, a 26 % improvement of the fatigue limit is observed, increasing from 65 MPa to 81 MPa for preload 1.These values should be compared to the fatigue limits for dense samples, i.e. 150 MPa [42] and 115 MPa [43][44][45] for horizontally and vertically built specimens, respectively.As a comparison of the fatigue limit without preload, Solberg et al. [46] obtained a fatigue strength of 73 MPa at 2 × 10 6 cycles for vertical specimens with porosity levels similar to this study.
The vertical specimens are generally considerably weaker and more brittle than the horizontal specimens, especially in this context with increased porosity.Therefore, preload 1, defined at 0.85 σ Y , is significantly lower for the vertical specimens (340 MPa) compared to the horizontal specimens (408 MPa).As a result, the influence of the preload on fatigue life is smaller for the vertical specimens compared to the horizontal ones, as the maximum stress in the subsequent fatigue cycles is close to the magnitude of the preload, resulting in a smaller impact.However, as the stress amplitude decreases, the influence of the preload increases, improving the fatigue limit by approximately 25 % for both the vertical and horizontal specimens.

Fractography
Fracture surfaces of horizontal fatigue specimens subjected to the same cyclic load with stress amplitude of 110 MPa, but different prior preloads, are shown in Fig. 13.As seen, although striations are not present, regions of crack initiation, crack propagation and final failure are still roughly identifiable.In fact, the crack usually initiates from an edge or inner defect and grows slowly at the beginning which makes the crack initiation region smoother compared to the other regions.The crack propagation region is characterized by a rougher surface next to the crack initiation region.The final failure region contains a substantial amount of pores which grow larger at the end of the fatigue life of the specimen.The difference in height is another characteristic feature for the final failure region.
Nevertheless, when there is no preload, the crack has initiated in the interior of the specimen (see Fig. 13a).The edge defects in the lower left corner and the one on the left surface in Fig. 13a had a strong influence on the failure of the specimen.The surfaces are susceptible to crack growth and a clear crack propagation from the defects can be seen on  these fracture surfaces.As a result, the defects have a detrimental effect on the fatigue life of these specimens.The fracture surface of the specimen subjected to preload 1, shown in Fig. 13b, have a crack initiation site from the large LOF defects as well.This disruption of crack growth is seen in the surface defects and especially in the inner defects marked in green in Fig. 13b.More crack arrest can be seen for these specimens since preload causes a favorable internal stress state which leads to higher resistance to crack propagation.As a result, the detrimental effect of the LOF defects is lowered and the fatigue life is increased significantly.Similar features are distinguishable on the fracture surface of the specimen subjected to preload 2, see Fig. 13c.A crack initiated from the surface defects marked in green in the lower right corner.However, the disruption in the crack growth from these defects is also noticeable which leads to longer fatigue life.The crack initiation region marked in yellow is smoother for this specimen as well compared to Fig. 13a, indicating a slower crack growth rate.This is explained by a phenomenon that cannot be seen in the image, namely the change in the internal stress states imposed by the preload.

Defects analysis
The imposed preloads on the specimens may alter the imperfections in the material, such as the shape of the LOF defects at the surface.The mean roundness is used to quantify this effect after preload.In total, 30 surface defects were investigated with SEM on the horizontal and vertical specimens.For the horizontal specimens, 10 surface defects were studied before and after preload 1 and an additional 10 surface defects were studied before and after preload 2. For the vertical specimens, 10 surface defects were investigated before and after preload 1.The mean roundness only slightly increased for all three categories, 0.7 % for the horizontal specimens after preload 1, 4.9 % for the horizontal specimens after preload 2 and 1.9 % for the vertical specimens after preload 1.The local tip radius was also considered in the analysis, with the SEM images analysed both before and after a preload, revealing no clear evidence of blunting.As an alternative approach, roundness measurements were subsequently employed to explore additional potential indications of blunting.
Some of the investigated defects are shown in Fig. 14 before and after loading.Here, the loading direction is horizontal in the picture and the LOF defects are oriented perpendicular to the loading direction.The  width of the surface defects slightly increased after loading while the height slightly decreased.This can be seen in Fig. 14a and Fig. 14b where a trapped powder particle with a diameter of approximately 40 μm, which corresponds well with the powder particle size in Fig. 1, could roll over to the other end of the defect after loading due to increased width.Overall, the change in shape and blunting effect for most of the defects after the preloading is insignificant and cannot explain the substantial improvement in fatigue performance.It should also be noted that, although the 2D inspection of defects reveals no blunting effect and only negligible change in defect size, further analysis of the 3D defects using CT could be of interest in future work [47].

Residual stress
The residual stresses were measured on the top and bottom surface of one vertical specimen and two horizontal specimens, before and after preload 1 and preload 2, see Fig. 15.The measurements were performed in three different directions, 0 • , 45 • and 90 • from the loading direction.As is observed from the XRD measurements, the applied preloads significantly influenced the residual stresses at the surfaces.That is, the tensile residual stresses on both sides of the specimens are reduced after preloading.The reduction is higher for preload 2 compared to preload 1, which is in agreement with the more pronounced improvement of the fatigue performance after preload 2 observed in Fig. 11a.It is noted that only the surface residual stress state has been measured.In fact, the specimens failed mainly with crack initiation from the surface (Section 3.3), which is reasonable given the large tensile residual stress state (Fig. 15) and the presence of surface defects (Section 3.4), suggesting that the surface residual stress is of highest importance.
The SWT mean stress correction [33] according to Eq. ( 2) was applied to quantify the effect of the reduction of tensile residual stress at the surface due to the preload on the fatigue limit.The correction predicts an increase in the fatigue limit of 14.7 % and 20.4 % after preload 1 and preload 2, respectively, for the horizontal specimens.For the vertical specimens, the fatigue limit increased by only 0.6 % after preload 1.It is important to note that the residual stress measurements are in macroscale, with a surface spot size of 2 mm in diameter.Local compressive residual stresses around defects may still be present without altering the global residual stress on the surface significantly.In addition, the surfaces of the horizontal and vertical specimens exhibit different microstructures due to the orientation of the build layers and the characteristic of the grains being elongated in the build direction.Hence, the influence of the preload on the global residual stress state on the surfaces of horizontal and vertical specimens may differ.Blinn et al. [48] have also demonstrated a difference in the impact of stress-relief heat treatment on the fatigue life of horizontal and vertical specimens, with a beneficial effect on the horizontal specimens and no pronounced difference for the vertical specimens.

Numerical simulation
The initial residual stress on the surfaces, see Fig. 6, is estimated from the XRD measurements in the 0 • direction for both horizontal and vertical specimens as σ x = 300 MPa.For the horizontal specimens, the global stress-strain curves are illustrated in Fig. 16a for no preload, preload 1 and preload 2 for an applied amplitude of 110 MPa as seen in Fig. 16b.As seen from Fig. 16a, elastic shakedown is obtained immediately after the preload and the subsequent cycles are purely elastic.
The FE contour plot in the figure shows the stress σ x in the loading direction after unloading from preload 2. In Fig. 16c, the resulting local stress-strain response at the edge of an elliptical surface defect is shown.As can be seen, small plastic deformation is seen even without the preload, followed by elastic shakedown.In the case with preload, more plastic deformation is evident with a subsequent small Bauschinger effect during unloading and elastic shakedown at lower stress values.From Fig. 16d, it is seen that mean stress reduces remarkably from 510 MPa (no preload) to 204 MPa after preload 1 and 60 MPa after preload 2, see Fig. 16d.Although the local stress-strain curve revealed a Bauschinger effect during reversed loading, its primary impact is on the local mean strain rather than the mean stress, given that the loading is force-controlled.Considering the study's emphasis on examining changes in local mean stress, the influence of the Bauschinger effect resulting from the selection of hardening parameters was intentionally overlooked.
The finite element model in Fig. 17 for the vertical specimen shows similar behaviour.The stress in the loading direction after preload 1 is illustrated together with the global and local stress responses.Here, a stress amplitude of 70 MPa is used.For both the vertical and horizontal models, a stress amplitude close to the fatigue limits was chosen in the numerical simulations to analyse the increase in fatigue strength due to the preload.As can be seen from Fig. 17d, the local mean stress at the edge of the surface defect decreased significantly from 475 MPa (no preload) to 109 MPa after preload 1.Hence, the major influence of the preload on the improved fatigue performance is attributed to the change in the local stress state around the defects.This explains the crack arrests around the LOF defects on the fracture surfaces and the longer fatigue lives for the specimens with preload despite the high density of, on beforehand, detrimental defects.
In both Fig. 16c and Fig. 17c, it can be seen that the initial stress at the edge of the surface defect is high with a magnitude of approximately 600-650 MPa.This is a result from the applied initial residual stress resulting in a local stress concentration.Here, viscoplasticity effects which could cause local stress relaxations are neglected.Several studies have shown that high local residual stresses are common in 316L Fig. 14.Surface defects on horizontal and vertical specimens before and after loading.The loading direction is the horizontal direction in the figure .stainless steel as a result of the PBF-LB process.Hu et al. [49] have shown that residual stresses from the PBF-LB process can reach 657 MPa locally in 316L.Another study by Waqar et al. [20] obtained residual von Mises stresses up to 475 MPa for PBF-LB fabricated 316L when no preheating was applied to the working plate.High residual stresses as a consequence of the PBF-LB process is presented in several other studies as well for different materials [50][51][52][53].Hence, we are assuming small or negligible stress relaxations in the material during the manufacturing process and thus viscoplasticity is omitted in the FE model.The local residual stresses around defects play a crucial role in fatigue performance.Blinn et al. [48] demonstrated that stress-relief heat treatment increases the fatigue strength of horizontally built specimens, attributed to improved defect tolerance.Several other studies [6,17,54,55] have also indicated the detrimental impact of tensile residual stresses in metal AM on the material's mechanical performance.
It is possible to estimate an approximate optimal preload value that maximizes the increase in fatigue limit using the FEM simulations.The results from the horizontal specimen demonstrate that preload 1 reduced the local mean stress from 510 MPa to 204 MPa, while preload 2 further decreased the mean stress to 60 MPa.This trend corresponds well with the observed increase in fatigue limits.Specifically, preload 1 increased the fatigue limit by 17 % compared to the case without preload, whereas preload 2 led to a 7 % increase compared to preload 1.As preload increases, the fatigue limit continues to rise incrementally, albeit with diminishing returns at each subsequent increment.This behavior is mirrored in the decrease in local mean stress.The rationale behind this trend is associated with higher preload levels storing more elastic energy, leading to a more substantial elastic unloading and subsequently reducing the local mean stress.However, the higher preload levels also come with an increased risk of damage and potential crack initiation, which could significantly impact fatigue performance.This concern is exemplified by the failure of vertical specimens under preload 2, highlighting the need to consider potential damage and crack initiation risks when employing higher preloads.It's important to note the absence of a damage model in the FE analysis.This limitation should be taken into account when interpreting the results and their practical implications.
Fig. 16d and Fig. 17d demonstrate that the influence of preloading is mainly attributed to the change in the local mean stress at the tip of the defect during cyclic loading.In Fig. 18, the influence of the initial surface residual stress from the PBF-LB manufacturing, on the mean stress at the tip of the defect after preloading is quantified based on the FEmodel.By comparing the No preload curve to the Preload 1 curve in Fig. 18a for the vertical specimen, the results show a high decrease in the local mean stress at the defect due to preloading regardless of the initial residual stress.However, the effect is larger for higher initial residual stresses.Similar results are obtained for the horizontal specimens as seen in Fig. 18b.In the absence of initial residual stress, Fig. 18b illustrates that preload 1 reduces the local mean stress more than preload 2. This difference can be attributed to the competing mechanisms between inducing local stresses from the preload itself and reducing local stresses during unloading from the preload.Specifically, the disparity between the magnitudes of the induced local stress at the defect tip and the reduced local stress is greater for preload 1 as opposed to preload 2 in the absence of initial residual stresses.Hence, in this scenario, the lower preload 1 proves to be more effective in reducing the local mean stress, while preload 2 induces more stress in the loading phase compared to preload 1, subsequently failing to reduce the stresses more than preload 1 during the unloading phase.However, as the initial residual stress increases, a transition point emerges at 50 MPa, and at higher values, preload 2 surpasses preload 1, becoming more effective in reducing the local mean stress.This shift is due to the fact that, with high initial residual stress, the stress at the defect tip does not undergo significant changes when subjected to a preload, as illustrated in Fig. 16c.The maximum local stress at the tip of the defect under preload 1 and preload 2 remains similar, close to 1000 MPa.The key distinction between the two preloads lies in the fact that more elastic energy is stored in preload 2, leading to a more significant reduction in local mean stress during unloading when compared to preload 1.
In Fig. 19, the influence of the applied stress amplitude, on the mean stress at the tip of the defect after preloading is studied.The simulations were performed for an initial residual stress of 300 MPa at the surface.As can be seen, the lower the applied stress amplitude, the larger the influence of the preload.This prevails for both vertical (Fig. 19a) and horizontal (Fig. 19b) specimens.On the contrary, the No preload and Preload 1 curves converge to the same local mean stress value for both the horizontal and vertical specimens as the stress amplitude is increased.This is explained by the stress amplitude simply being the same value corresponding to the magnitude of the preload.Hence, no influence from the preload is observed once the stress amplitude is increased to an extent where the remaining cycles have a maximum stress value corresponding to the preload value.If the stress amplitude is

Fig. 2 .Fig. 3 .
Fig. 2. Clamped blocks on both sides to prevent deformation during cutting with EDM and a deformed block after machining due to residual stresses.

Fig. 4 .
Fig. 4. The experimental setup for (a) uniaxial tensile test and (b) uniaxial fatigue test; and (c) the magnitudes of preload 1 and preload 2 prior to the fatigue tests.

Fig. 5 .
Fig. 5.The setup for the XRD analysis: three specimens (one vertical and two horizontal) were used to measure the residual stresses on a spot size of 2 mm in diameter in three different directions.

Fig. 6 .
Fig. 6.Boundary conditions and initial residual stress state in the finite element model.

Fig. 9 .
Fig. 9. SEM images of LOF defects and gas pores of a horizontally built specimen from block H7 on (a) polished surface and (b) as-built surface.

Fig. 12 .
Fig. 12.The staircase method used to calculate the fatigue limit of PBF-LB made 316L SS with (a) horizontally and (b) vertically built specimens.

Fig. 13 .
Fig. 13.Fracture surface of specimens with (a) no preload, (b) preload 1 and (c) preload 2 all tested at the same stress amplitude of 110 MPa.The number of cycles to failure and the block from which the specimen is manufactured from are indicated below each fracture surface.

Fig. 15 .
Fig. 15.The residual stresses on the top and bottom surface of a vertical specimen and two horizontal specimens before and after preload 1 and preload 2 in the three different directions, 0 • , 45 • and 90 • from the loading direction.

Fig. 16 .
Fig. 16.The stress state in a horizontal specimen with and without preloading.The global response in terms of stress-strain and stress-cycles curves are shown in (a) and (b), respectively, while the local stress-strain and stress-cycles curves at the tip of the surface defect are shown in (c) and (d), respectively.

Fig. 17
Fig. 17.The stress state in a vertical specimen with and without preloading.The global response in terms of stress-strain and stress-cycles curves are shown in (a) and (b), respectively, while the local stress-strain and stress-cycles curves at the tip of the surface defect are shown in (c) and (d), respectively.

.
Fig. 17.The stress state in a vertical specimen with and without preloading.The global response in terms of stress-strain and stress-cycles curves are shown in (a) and (b), respectively, while the local stress-strain and stress-cycles curves at the tip of the surface defect are shown in (c) and (d), respectively.

Table 1
Manufacturing process parameters.