Olivier Andreau
email: andreau.olivier@gmail.com

Etienne Pessard

Imade Koutiri

Patrice Peyre

Nicolas Saintier

Influence of the position and size of various deterministic defects on the high cycle fatigue resistance of a 316L steel manufactured by laser powder bed fusion

Keywords: Laser Powder Bed Fusion, Austenitic stainless steel, Fatigue, Defect, Porosity

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Influence of the position and size of various deterministic defects on the high cycle fatigue resistance of a 316L steel manufactured by laser powder bed fusion

Introduction:

Among the metal additive manufacturing techniques, Laser Powder Bed Fusion (LPBF) is widely recognized as one of the most promising method for the industry of the future, due to the attractive characteristics of built parts including: a high degree of complexity, a good spatial resolution (around 0.1 mm precision), and good mechanical resistance under static loading [START_REF] Wohlers | 3D Printing and Additive Manufacturing State of the Industry[END_REF]. In addition, the growing understanding of the link between process parameters and microstructures open the field of microstructure engineering, allowing, for example, the control of local textures or grain sizes [START_REF] Andreau | Texture control of 316L parts by modulation of the melt pool morphology in selective laser melting[END_REF][START_REF] Niendorf | Highly anisotropic steel processed by selective laser melting[END_REF]. For this reason, the range of applications is continuously growing up on a large range of materials, including recently complex metals to process with lasers like pure copper [START_REF] Colopi | Limits and solutions in processing pure Cu via selective laser melting using a high-power single-mode fiber laser[END_REF].

However, it is also well known that the fabricated parts without post processing are likely to contain defects including: a high roughness, internal pores due to lacks-of-fusion or occluded gas [START_REF] Kasperovich | Correlation between porosity and processing parameters in TiAl6V4 produced by selective laser melting[END_REF], and possible hot-cracking phenomena for instance on a range of nickel-based superalloys [START_REF] Wang | Selective laser melting of the hard-to-weld IN738LC superalloy: Efforts to mitigate defects and the resultant microstructural and mechanical properties[END_REF] or aluminium alloys. Such defects, and especially those promoting stress raisers like surface roughness and pores can promote early fatigue crack initiations and severely affect the material's resistance under cyclic loading [START_REF] Mower | Mechanical behavior of additive manufactured, powder-bed laserfused materials[END_REF]. For this reason, as-built 316L LPBF samples usually exhibit lower fatigue resistance than conventionally processed (forged) materials. The fine LPBF microstructure in itself, can also influence the fatigue resistance, small grains and/or tiny solidification cells (around 1 µm size) favouring dislocations anchoring with a Hall-Petch-like effects, and a possible increase of yield strength and fatigue limit.

Compared with other as-built alloys (titanium based, nickel-based …), 316L stainless steel has been observed to reach outstanding mechanical monotonous properties, with an optimum balance between good ductility (usually more than 40 % elongation after LPBF), and elevated yield or ultimate strengths (respectively more than 550 MPa and 650 MPa) [START_REF] Wang | Additively manufactured hierarchical stainless steels with high strength and ductility[END_REF][START_REF] Wang | Crystallographic-orientation-dependent tensile behaviours of stainless steel 316L fabricated by laser powder bed fusion[END_REF][START_REF] Zhang | Fatigue and fracture behaviour of laser powder bed fusion stainless steel 316L: Influence of processing parameters[END_REF]. The explanation for such a behaviour is not fully achieved but could come from the fine microstructure, with typical inter-cell distances around 1 µm [START_REF] Marchese | Influence of heat treatments on microstructure evolution and mechanical properties of Inconel 625 processed by laser powder bed fusion[END_REF][START_REF] Hardes | Cavitation erosion resistance of 316L austenitic steel processed by selective laser melting (SLM)[END_REF] combined with a high dislocation density (around 10 15 m -2 [START_REF] Gorsse | Additive manufacturing of metals: a brief review of the characteristic microstructures and properties of steels, Ti-6Al-4V and highentropy alloys[END_REF]). In-depth analysis of the role of the dislocation network and nano-twinning during deformation of LPBFed 316L parts was done by Liu et. al [START_REF] Liu | Dislocation network in additive manufactured steel breaks strength-ductility trade-off[END_REF]. Another important aspect to mention is that 316L is believed to be a rather defect-tolerant material due to its high ductility that promotes a low notch sensitivity, as mentioned by Riemer et al [START_REF] Riemer | On the fatigue crack growth behavior in 316L stainless steel manufactured by selective laser melting[END_REF].

Recent investigations have shown that post-LPBF surface processing of a 316L steel can significantly improve mechanical properties, especially in fatigue [START_REF] Elangeswaran | Effect of post-treatments on the fatigue behaviour of 316L stainless steel manufactured by laser powder bed fusion[END_REF][START_REF] Shrestha | Fatigue behavior of additive manufactured 316L stainless steel parts: Effects of layer orientation and surface roughness[END_REF]. On the other hand, thermomechanical post processing such has HIP or high temperature heat treatments have proven to worsen the fatigue properties of 316L LPBF [START_REF] Riemer | On the fatigue crack growth behavior in 316L stainless steel manufactured by selective laser melting[END_REF][START_REF] Leuders | On the fatigue properties of metals manufactured by selective laser melting -The role of ductility[END_REF]. This was explained by the recrystallization phenomenon occurring at high temperature, and resulting in a strong reduction of dislocation density [START_REF] Kong | Mechanical properties and corrosion behavior of selective laser melted 316L stainless steel after different heat treatment processes[END_REF][START_REF] Kong | Bio-functional and anti-corrosive 3D printing 316L stainless steel fabricated by selective laser melting[END_REF]. In that case, even if thermal or thermomechanical post-treatments reduce the dislocation density, they do not significantly increase the ductility (+10%) of the material, while reducing noticeably its yield strength (-30%) [START_REF] Leuders | On the fatigue properties of metals manufactured by selective laser melting -The role of ductility[END_REF]. Heat treated materials will thus have relatively lower high cycle fatigue performances than as-built samples, for similar surface finish. In turn, according to Riemer et al. [START_REF] Riemer | On the fatigue crack growth behavior in 316L stainless steel manufactured by selective laser melting[END_REF] and Leuders et al. [START_REF] Leuders | On the fatigue properties of metals manufactured by selective laser melting -The role of ductility[END_REF], LPBF and machined 316L steel may be used without additional post-processing stages.

Considering various reported works on the fatigue behaviour of LPBF-ed 316L steel, a large scattering of fatigue limits at 10 6 cycles can be evidenced, for rather similar process conditions, but different surface finish. For instance, at R=-1 stress ratio, endurance limits vary between 200 MPa and 350 MPa [START_REF] Mower | Mechanical behavior of additive manufactured, powder-bed laserfused materials[END_REF][START_REF] Elangeswaran | Effect of post-treatments on the fatigue behaviour of 316L stainless steel manufactured by laser powder bed fusion[END_REF][START_REF] Leuders | On the fatigue properties of metals manufactured by selective laser melting -The role of ductility[END_REF][START_REF] Zhang | High cycle fatigue and ratcheting interaction of laser powder bed fusion stainless steel 316L : Fracture behaviour and stressbased modelling[END_REF], with a 200 MPa fatigue limit for as-built condition (Ra = 7 µm) versus 350 MPa after surface machining (Ra= 0.5 µm) [START_REF] Elangeswaran | Effect of post-treatments on the fatigue behaviour of 316L stainless steel manufactured by laser powder bed fusion[END_REF]. This traduces the dominant effect of surface roughness even for a material usually considered as a defect tolerant material.

For low roughness, the sub-surface and internal defects will drive the fatigue performances. Zhang et al. [START_REF] Zhang | Fatigue and fracture behaviour of laser powder bed fusion stainless steel 316L: Influence of processing parameters[END_REF] have evidenced that the fatigue properties of 316L fabricated in LPBF are impacted above 0.5 % of internal porosity, without discussing precisely the size threshold at which a defect can be impactful.

Such high porosity thresholds tend to indicate that internal porosity in 316L parts will have a low impact on fatigue properties. However, the fatigue resistance of materials containing defects is mostly driven by their critical defects population. Apart from its shape and tortuosity, an unique critical defect (ie an artificially introduced defect that will drive and overcome all other possible fatigue failure mechanisms) will combine two major characteristics: a sufficient size and a reduced distance to the surface.

Murakami's work in the field combined those two factors [START_REF] Murakami | Metal Fatigue : Effect of Small Defects and Nonmetallic Inclusions[END_REF] by introducing a surface/internal defect discrimination method, in addition to a higher harmfulness coefficient 𝐶 for surface defects. The stress intensity factor calculated for a stress range 𝛥𝜎 with a critical defect of size √𝐴𝑟𝑒𝑎 is given Eq. 1.

𝛥𝐾 = 𝐶 * 𝛥𝜎 √ 𝜋√𝐴𝑟𝑒𝑎

Eq. 1

A defect with radius 𝑟 at a distance 𝑑 between its center and the surface, is considered to be at the surface if the ratio 𝑟 𝑑 ⁄ is over 0.8. The 𝐶 coefficients 0.5 (internal defect) and 0.65 (surface defects) that are applied in the calculation of their respective stress intensity factors are equivalent to considering identical harmfulness between surface defects of a given size and 67% larger internal defects.

Romano et al. [START_REF] Romano | Fatigue properties of AlSi10Mg obtained by additive manufacturing : Defect-based modelling and prediction of fatigue strength[END_REF] and Le et al. [START_REF] Le | Interpretation of the fatigue anisotropy of additively manufactured TA6V alloys via a fracture mechanics approach[END_REF] have both shown that it was possible to link different defect populations, with various statistical size distributions, to the fatigue properties of an AlSi10Mg and a Ti-6Al-4V alloy respectively. A correlation was also shown between stress intensity factors of the most detrimental defects detected by computed tomography and associated fatigue resistance.

Last, recent works by Andreau et al. [START_REF] Andreau | A competition between the contour and hatching zones on the high cycle fatigue behaviour of a 316L stainless steel: Analyzed using X-ray computed tomography[END_REF] on LPBF-ed 316L have shown a systematic initiation of fatigue cracks on surface defects, despite the presence of 4 to 10 times larger internal defects in the bulk of small machined and polished cylindrical fatigue samples. Although those defects had a similar shape, only internal porosities of more than 400 µm equivalent diameter were shown to impact the fatigue properties. Another interesting result was the possibility to achieve high fatigue limits (500 MPa) at 10 6 cycles and R=0.1 stress ratio with totally free from defects samples.

Following this literature review, it appears that the two main factors that turn a defect into a critical defect for fatigue, need to be decorrelated in order to further analyse and model the respective fatigue strength sensitivity to each one of these parameters. Additionally, the need of more reference data for defect-free parts is also believed to be crucial in order to assess globally the fatigue performances of LPBF 316L parts.

In the current work, to facilitate the analysis of defects harmfulness, artificial pores were generated on purpose inside LPBF samples using the same early approach by Gong [START_REF] Gong | Generation And Detection Of Defects In Metallic Parts Fabricated By Selective Laser Melting And Electron Beam Melting And Their Effects On Mechanical Properties[END_REF], and the same procedure by Bonneric et al. [START_REF] Bonneric | Investigation of the sensitivity of the fatigue resistance to defect position in aluminium alloys obtained by Selective laser melting using arti fi cial defects[END_REF]. In a first part, an optimization of defect shape was made, with the objective of obtaining as spherical as possible lacks-of-fusion with various submillimeter diameters and controlled distances from the surface. Then, fatigue tests were carried out to assess the influence of defect position and size. Corresponding results were compared with those obtained on fully optimized as-built LPBF 316L parts containing almost no porosity, and considered as a reference material. The global objective of the work was to characterize precisely the competition between surface and internal defects by creating parts containing deterministic defects.

Methods and tools

LPBF manufacturing of samples containing deterministic defects

The samples were manufactured using a SLM 125 HL machine (from SLM Solutions GmbH), which was equipped with a 400 W Nd:YAG gaussian laser and argon gas shielding, with less than 400 ppm O2. The 316L powder feedstock used in this study is described elsewhere [START_REF] Andreau | Texture control of 316L parts by modulation of the melt pool morphology in selective laser melting[END_REF]. Optimized building parameters were determined by a parametric study [START_REF] Andreau | Nocivité en fatigue et contrôle de défauts produits par fabrication additive[END_REF] for a 30 µm layer thickness and a 73 µm (at 1/e 2 ) spot diameter. Contour and hatching laser parameters are given in Table 1. A meander scanning strategy [START_REF] Casati | Microstructure and Fracture Behavior of 316L Austenitic Stainless Steel Produced by Selective Laser Melting[END_REF] was used to avoid any overlap between distinct parts that can induce pores [START_REF] Carter | The influence of the laser scan strategy on grain structure and cracking behaviour in SLM powder-bed fabricated nickel superalloy[END_REF][START_REF] Catchpole-Smith | Fractal scan strategies for selective laser melting of 'unweldable' nickel superalloys[END_REF]. A scan rotation after each layer was set at 33°. The forbidden scanning angles were set at ±45° versus the shielding gas direction to prevent the interaction between the laser and the vapor plume.

Power (W)

Scanning speed (mm.s - Manufacturing deterministic spherical defects with LPBF requires a specific optimization step to ensure defects geometries as close as possible from CAD files. This is particularly important for the contour parameters outlining the external defect shape. Contour parameters sets were thus used on both the outside (external contour) and the inside (internal contour) of the parts. (Figure 1 a)). Corresponding parameters are given in Table 1.

For all overhanging areas inclined by less than 59° from the X-Y plane, specific downskin parameter sets were applied. This low-energy parameter set (Table 1) replaces classic contour and hatching laser parameters, in order to minimize the energy (~ P/V) deposited by the laser in overhanging areas (Figure 1 b)). Favouring small melt pools in overhanging areas limits their collapse, and reduces the need for supporting [START_REF] Mertens | Optimization of Scan Strategies in Selective Laser Melting of Aluminum Parts With Downfacing Areas[END_REF][START_REF] Chen | Improving additive manufacturing processability of hard-toprocess overhanging structure by selective laser melting[END_REF][START_REF] Andreau | Deterministic defect generation in selective laser melting : parametric optimization and control[END_REF], the absence of internal supports being mandatory for the spherical defects. For every overhang zone included in the downskin criterion, laser parameters of contour and hatching were shifted to their downskin equivalents for the next 5 layers (150 µm), according to the values given Table 1.

Preparation of the fatigue samples

Two formats of fatigue samples have been manufactured. First, small fatigue samples (Figure 2 a))

were designed to minimise the probability (statistically) of a critical manufacturing defect, with a gauge volume of 48 mm 3 . Second, larger fatigue samples (Figure 2 b)) were used to characterize the influence of internal deterministic defects (gauge volume: 283 mm 3 ). The large fatigue samples pertain to the ISO 1099:2017(E) norm. All the fatigue samples were obtained from LPBF square based blocks (small samples) or cylinders (large samples) manufactured vertically in the machine, after machining them to the required dimensions. The vertical manufacturing direction was chosen as to minimize the heterogeneities of the local applied stresses in the most loaded area of the deterministic defects, as the smoothness and symmetry of the manufactured defects was higher in the plane normal to the building direction. The machining step was chosen to reduce the as-built surface roughness that is known to impact the fatigue properties [START_REF] Elangeswaran | Effect of post-treatments on the fatigue behaviour of 316L stainless steel manufactured by laser powder bed fusion[END_REF], from a Ra of 5-10 µm down to down to 0.1 µm after polishing. The machining residual stresses were then reduced with a 2 h thermal treatment at 350°C under argon atmosphere before furnace cooling.

A total of 7 optimized small samples (S-1 to S-7) were manufactured, as well as 24 large samples containing various deterministic defects. Among the large fatigue samples, 3 deterministic defect dimensions were chosen, along with 3 distances to the surface (Figure 2 c)). Their nomenclature and number are summarized on Table 2. The deterministic defect dimensions were chosen as to be larger than the grain size (typically comprised between 10 and 140 µm, as observed and detailed in previous work [START_REF] Andreau | A competition between the contour and hatching zones on the high cycle fatigue behaviour of a 316L stainless steel: Analyzed using X-ray computed tomography[END_REF]), while being small enough to have a minimal impact on the stress distribution by reducing the total area of the gauge. Moreover, the deterministic defects of diameter 430 µm have a √𝑎𝑟𝑒𝑎 of 380 µm, which is equal to the natural defect threshold size at which crack initiation occurred internally in previous work [START_REF] Andreau | A competition between the contour and hatching zones on the high cycle fatigue behaviour of a 316L stainless steel: Analyzed using X-ray computed tomography[END_REF] for the same material (defect conglomerate visualized in Figure 5 d)). The various distances shown in Table 2 correspond to the length between the surface and the center of the defect.

They correspond to a defect placed: (i) in the center of the sample, (ii) offcentered by a half of the gauge radius, (iii) at one defect diameter from the surface, and (iv) one radius from the surface (Figure 2 c)).

The thinnest distance to the surface obtained was thus 215 µm, i.e. the radius of the middle sized deterministic defect. A batch of 6 specimens with large section and without any deterministic defects were added to be used as a reference for large specimen and noted L-i.

Characterization tools

EBSD analysis was carried out on a Philips XL 40 Scanning Electron Microscope on polished cross sections, with a resolution of 1 µm per pixel. Additional EBSD parameters can be found in previous work [START_REF] Andreau | Texture control of 316L parts by modulation of the melt pool morphology in selective laser melting[END_REF].

µ-CT characterization was carried out on some dense samples and samples containing deterministic defects, with voxel sizes of 5x5x5µm 3 and 6.4x6.4x6.4 µm 3 respectively, by varying the distance between the object and the detector. Defects with a volume inferior than 27 voxels were not considered. Additional µ-CT parameters can be found in previous work [START_REF] Andreau | A competition between the contour and hatching zones on the high cycle fatigue behaviour of a 316L stainless steel: Analyzed using X-ray computed tomography[END_REF].

High cycle fatigue testings were carried out on small samples with a Rumul Testronic resonant machine with a load ratio R=0.1 at 65 Hz. The large samples were tested on a Zwick resonant machine at the same load ratio at a frequency of around 90 Hz. All samples were tested in air at ambient temperature, using the same step loading method, first described by Maxwell and Nicholas [START_REF] Maxwell | A rapid method for generation of a Haigh Diagram for high cycle fatigue[END_REF] and used in previous studies [START_REF] Andreau | A competition between the contour and hatching zones on the high cycle fatigue behaviour of a 316L stainless steel: Analyzed using X-ray computed tomography[END_REF]. The method consisted in imposing a given stress level at each sample. If the sample did not fail before reaching 10 6 cycles, the maximum applied stress was increased by 20 MPa and the cycle count was reseted. The stop criterion (failure) was considered for the total failure of the sample, or a 1 Hz drop in the loading frequency. The difference in loading frequency between the two machines was considered to have a negligible impact on the fatigue properties. The fracture surfaces were analysed on a Zeiss EVO MA10 Scanning Electron Microscope in secondary electron mode.

Results

Microstructural and preliminary characterization

Some of the manufactured optimized samples were initially characterized by EBSD and metallography, in order to lay the microstructural environment of the study.

The observations showed partially elongated grains (Figure 3 a)) along the fabrication direction (Z axis), that are induced by epitaxial growth [START_REF] Thijs | Fine-structured aluminium products with controllable texture by selective laser melting of pre-alloyed AlSi10Mg powder[END_REF][START_REF] Yadroitsev | Single track formation in selective laser melting of metal powders[END_REF]. A grain shape anisotropy is evidenced by the smaller grain size (30 µm in equivalent diameter) in the plane perpendicular to the fabrication direction (X-Y plane) than in the plane parallel to the loading direction (50 µm) as seen in Figure 3 b) and c). A small texture (intensity ~3) can be observed with the preponderant [001] grain orientation (red color) along the X axis (Figure 3 a) and b)), in accordance with previous studies [START_REF] Andreau | Texture control of 316L parts by modulation of the melt pool morphology in selective laser melting[END_REF][START_REF] Wang | Crystallographic-orientation-dependent tensile behaviours of stainless steel 316L fabricated by laser powder bed fusion[END_REF][START_REF] Shamsujjoha | High Strength and Ductility of Additively Manufactured 316L Stainless Steel Explained[END_REF]. The numerous subgrain boundaries and the inhomogeneous colors in the grains are the result of a high dislocation density that accommodates crystallographic deformation, which is thought to be linked to the high thermal gradients and rapid solidifications rates [START_REF] Scipioni Bertoli | Stability of cellular microstructure in laser powder bed fusion of 316L stainless steel[END_REF] of the LPBF process. Finally, a porosity analysis performed by tomography and metallography showed porosity rates of about 0.01%. In this work, the natural defect dimensions will be described using the common Murakami

√𝑎𝑟𝑒𝑎 parameter [START_REF] Murakami | Metal Fatigue : Effect of Small Defects and Nonmetallic Inclusions[END_REF]. The defect population was measured in 70 mm 3 of material using X-ray tomography, and the parameters used can be found elsewhere [START_REF] Liu | Effect of scanning speed on the microstructure and mechanical behavior of 316L stainless steel fabricated by selective laser melting[END_REF]. The defect detection threshold was set at 15 µm in √𝑎𝑟𝑒𝑎. The volume was then subdivided in 30 subvolumes and the largest defect of each volume was measured, according to the Gumbel method [START_REF] Gumbel | The Return Period of Flood Flows[END_REF], as in the work of Romano et al. [START_REF] Romano | Materials & Design Quali fi cation of AM parts : Extreme value statistics applied to tomographic measurements[END_REF]. The defect distribution showed that among the 405 pores detected, no pores with a root area superior than 50 µm were observed (Figure 3 c)). A finer 2D metallography analysis, with submicronic resolution, carried out on 144 mm² of polished X-Y cross sections, revealed that among the 1150 pores found, 97% had a √𝑎𝑟𝑒𝑎 under 10 µm. Those manufacturing parameters sets were used in recent studies [START_REF] Liu | Effect of scanning speed on the microstructure and mechanical behavior of 316L stainless steel fabricated by selective laser melting[END_REF] and showed density rates over 99.99%.

Monotonic tensile test of heat relieved samples manufactured vertically using the hatching parameters sets of this study showed a 583±37 MPa maximum tensile strength, 448±32 MPa yield strength, with more 54±4% elongation [START_REF] Andreau | Nocivité en fatigue et contrôle de défauts produits par fabrication additive[END_REF]. Those results were in accordance with the common mechanical properties of LPBF 316L from literature [START_REF] Wang | Additively manufactured hierarchical stainless steels with high strength and ductility[END_REF][START_REF] Pham | Twinning induced plasticity in austenitic stainless steel 316L made by additive manufacturing[END_REF][START_REF] Montero-Sistiaga | Microstructure evolution of 316L produced by HP-SLM (high power selective laser melting)[END_REF]

Deterministic defect generation validation

In order to validate the method, a range of test deterministic pores were analysed with optical microscopy. Figure 4 a) reveals the various melt pools around an ovoid deterministic pore after etching and compares it to the 3D model. A non-sphericity on the upper part of the defect is evidenced by a melt-pool collapse, as well as a roughness increase, linked to the powder grains sticking. The microstructural analysis in EBSD (Figure 4 b)) reveals that the grain morphologies and sizes directly reflect the parameter sets used to manufacture the defects. The small grains on the top of the pore correspond to the downskin hatching parameter area realized with low volumetric energy. In this area, grains are smaller in size and more equiaxial than in the rest of the sample. As this area is located on the top of the pore, it was not believed to have an impact on the mechanical properties if a crack were to initiate on the largest pore section. The outline of the contour scan can also be observed around the deterministic defects, with slightly smaller grains than in a fully dense part. Indeed, due to the perpetual shifts in the laser scanning directions, the contour zones offer less opportunity for epitaxial growth than the hatching zones. In addition, it was observed in previous work [START_REF] Andreau | A competition between the contour and hatching zones on the high cycle fatigue behaviour of a 316L stainless steel: Analyzed using X-ray computed tomography[END_REF] that the grains usually grow perpendicularly to the scanning direction in the contour areas. A number of indents were realized in the hatching and in the contour zones and revealed HV0.5 hardness values of 238±7 and 247±6 HV respectively. One can attribute this slightly higher hardness in the contour areas to the locally smaller grain size, via the Hall-Petch effect. This smaller grain size (<50 µm) is believed to be linked to the solidification conditions of the contour zones that are different from the bulk zones X-ray computed tomography observations were used for the 3D visualisation of the manufactured defects. The 3D reconstructions of deterministic defects (red) with target diameters of 900, 500 and 250 µm are shown in Figure 5 a) to c). The satellites pores (green) are much smaller than deterministic pores and were assumed to have a negligible impact on the mechanical properties. Those undesirable pores might have been be created by imperfect melt pool overlap in the contour areas, or instabilities in the melt pools in contour mode. The deterministic defects created with the method are highly symmetrical and must be considered as model defects. The natural lacks-of-fusion are much more irregular and tortuous in shape (Figure 5 d)). However, as in natural lacks-of-fusion, the deterministic defects are filled with powder, as can been seen in the reconstruction in Figure 5 c). The mechanical contribution of the powder in the defects was considered negligible. The deterministic defect generation method can be used successfully to create artificial pores of sizes in the range of 150 to 1000 µm, at any position in the bulk of a sample [START_REF] Andreau | Nocivité en fatigue et contrôle de défauts produits par fabrication additive[END_REF]. The variability in height and width were estimated at ±50 µm and ±20 µm for the largest pores. Defects with heights of 150 µm and less could not be manufactured repetitively, as their dimensions were too close from the powder dimensions (20-60 µm) and the melt pool dimension variability. As no internal crack initiation was observed for natural defects measuring less than 300 µm [START_REF] Andreau | A competition between the contour and hatching zones on the high cycle fatigue behaviour of a 316L stainless steel: Analyzed using X-ray computed tomography[END_REF], this defect generation method was considered sufficient to characterize realistically the impact of artificial defects.

Fatigue results

All the fatigue samples tested broke inside the gauge, after more than 1 step, except the sample R430-3. They were analysed post-mortem, in order to observe the crack initiation area. The sizes of the critical defects (natural or deterministic) were identified by their √𝑎𝑟𝑒𝑎 in the X-Y plane, perpendicular to the loading direction. All the fatigue results are summarized in Table 3.

Sample

Fatigue samples without deterministic defects

For all the specimens without artificial defect, crack did initiate from the surface. Among the optimized (small samples), two main failure origins were identified and corresponded to distinct groups in terms of fatigue performance. As indicated in Figure 6, samples S-1 and S-3 broke at stresses of 320

MPa (1 step) and 460 MPa (4 steps) respectively, whereas all the other samples survived for at least 9

steps and broke at a maximum stress of 560 MPa and above. The fracture surface analysis of samples S-1 and S-3 revealed that the cracks initiated on surface pores (Figure 7). Those pores were identified as lacks-of-fusion because of their irregular shape and the presence of ripples (Figure 7 b)), suggesting insufficient melt pool overlap. As the 137 µm defect was far larger than the observed pores in preliminary observations, it was considered to be an uncommon event of the manufacturing process. Its flatness along the Z direction could indicate a lack-of-fusion behind a large ejected particle, as observed in the literature [START_REF] Kasperovich | Correlation between porosity and processing parameters in TiAl6V4 produced by selective laser melting[END_REF]. The 23 µm defect was in the range of the usual defects root area in the bulk. The other 5 samples (S 2, 4, 5, 6, 7) did not show any critical pores at the surface, or even internally. In that case, it is supposed that the crack initiation occurred due to microstructural effects, i.e. within a grain, a grain boundary, or an inter-cell boundary. Some evidence of shear facets with dimensions corresponding to the grain size can indeed be observed in Figure 8 a) and b) around the crack initiation zone. Other samples did not exhibit large sheared facets around the crack initiation zones, but exhibited fine and angular zones (Figure 8 c) to f)) whose geometry shows strong similitude with subgrain boundaries in LPBF samples [START_REF] Andreau | Texture control of 316L parts by modulation of the melt pool morphology in selective laser melting[END_REF]. Similar observations were made by Elangeswaran et al. [START_REF] Elangeswaran | Effect of post-treatments on the fatigue behaviour of 316L stainless steel manufactured by laser powder bed fusion[END_REF], with no critical pores observed in the crack initiation areas. In their work, Zhang et al. [START_REF] Zhang | High cycle fatigue and ratcheting interaction of laser powder bed fusion stainless steel 316L : Fracture behaviour and stressbased modelling[END_REF] suggested the occurrence of crack branching around clustered oxide inclusions in 316 L LPBF fatigue loaded samples after HIP treatment. However, no trace of inclusions were found around the crack initiation zones in the S samples after elemental analysis. Among the large samples without artificial defects (L-1 to 6), crack initiation systematically occurred on measurable defects. All the critical defects were small in root area (<50 µm), with round shapes (Figure 9). An elemental analysis revealed the presence of silicon around some of those defects, suggesting the presence of inclusions already present in the feedstock [START_REF] Casati | Microstructure and Fracture Behavior of 316L Austenitic Stainless Steel Produced by Selective Laser Melting[END_REF]. In some cases, those defects can also be severely oxidized spatter generated during the manufacturing process and contaminating the powder bed [START_REF] Gunenthiram | Experimental analysis of spatter generation and melt-pool behavior during the powder bed laser beam melting process[END_REF]. In both instances, improper melt pool wetting can occur on these particles, resulting in local stress-raisers like pores.

Fatigue samples containing deterministic defects

Among the samples with deterministic defects, the C210 set also showed cracks originating from accidental defects at the surface. Figure 10 a) and b) show that the crack initiation occurred on a lack of fusion defect, despite the presence of the much larger deterministic defect at the center of the fracture surface.

On the contrary, crack initiation always occurred on centered deterministic pores for the sets C430 and C850 (Figure 10 c) to f)), with larger dimensions (381 and 753 µm in √𝑎𝑟𝑒𝑎 respectively), and no crack initiation was observed on the satellite pores. In those cases, the crack propagated all around the deterministic defects, resulting in large fisheye-like fracture surfaces. It is likely that the crack initiation occurred in multiple areas around the deterministic pores, where the stress concentration is higher, and that all the micro cracks created connected during the propagation phase. This is suggested by the local crack initiation and propagation areas in the close up in Figure 10 g) and h), on the periphery of the deterministic pore. This observation is also sustained by the lines surrounding the large deterministic pore, that are positioned between local propagation zones, such as in Figure 10 g). These figures also evidence that the layer by layer construction of the internal defect induce roughness on the internal surface of the defect, that generate heterogeneous local stress concentrations that may promote multicrack inititation. The three sample sets containing off-centered medium sized deterministic defects also showed a crack initiation occurring on the artificial defect (Figure 11 a) to c)). Most of the samples also exhibited a fisheye-like pattern, but some samples in R430 and D430 sets had highly asymmetric crack propagation (Figure 11 d)), contrarily to what could be expected from the literature [START_REF] Murakami | Metal Fatigue : Effect of Small Defects and Nonmetallic Inclusions[END_REF]. This observation could be linked to the stress field distribution, where theoretical stresses are higher on the thin ligament side. Performance-wise, no significant differences in fatigue endurance can be observed between the samples containing off-centered defects (R430, D430 and M430). In a similar manner, a centered defect (C430 set) shows very little impact on the fatigue properties. Indeed, the Figure 12 only displays a 10%

higher maximum stress at 10 6 cycles for the centered defects, but this observation could be offset by the high error bars. However, a noticeable performance increase can be noted when comparing with the internal natural defect from previous work (Figure 12). The very thin ligament size (110 µm) along with the tortuous shape of the natural defect (Figure 5 d)) could have impacted the fatigue properties.

Discussion

All of the tests carried out in this study are reported in a Kitagawa diagram in Figure 13, along with the tests from previous work [START_REF] Andreau | A competition between the contour and hatching zones on the high cycle fatigue behaviour of a 316L stainless steel: Analyzed using X-ray computed tomography[END_REF]. First, it must be emphasized that the fatigue endurance at 10 6 cycles obtained for the small optimal samples is extremely high in the absence of critical defects. To the knowledge of the authors, the average of 568 ±12 MPa found for the small samples where the crack initiated in the microstructure is the highest in the literature for 316L LPBF tested at R=0.1. Usual results for this material are in the 300-400 MPa range [START_REF] Zhang | Fatigue and fracture behaviour of laser powder bed fusion stainless steel 316L: Influence of processing parameters[END_REF][START_REF] Spierings | Fatigue performance of additive manufactured metallic parts[END_REF]. The extrapolation of the measurements performed by Elangeswaran et al. [START_REF] Elangeswaran | Effect of post-treatments on the fatigue behaviour of 316L stainless steel manufactured by laser powder bed fusion[END_REF] on LPBF 316L at R=-1 to R=0.1 using the Gerber equation is however be extremely close (530 MPa fatigue limit at 2x10 6 cycles). For 316L LPBF-HIP [START_REF] Zhang | High cycle fatigue and ratcheting interaction of laser powder bed fusion stainless steel 316L : Fracture behaviour and stressbased modelling[END_REF] or 316L laminate [START_REF] Mohammad | Fatigue Life for Type 316L Stainless Steel under Cyclic Loading[END_REF] the uniaxial fatigue limits at 10 6 cycles and R=0.1 are usually around 360 MPa and 440

MPa respectively.

The very low fatigue strength variability (12 MPa) at 10 6 cycles in the absence of defect also indicates that the failure mechanisms involved in those 5 samples are likely to be identical. The authors indeed observed similar fracture surfaces and had a fairly low porosity rate in as-built samples. In the current study, the absence of critical defects was favoured by the optimized parameters, as well as a reduced gauge volume. The remaining defects were measured to be in the 10-50 µm range versus a typical grain size in the axial direction of 50 µm and larger grains above 100 µm. The common fatigue life theory by Murakami [START_REF] Murakami | Metal Fatigue : Effect of Small Defects and Nonmetallic Inclusions[END_REF] shows that fatigue crack initiation requires the presence of a defect larger than a certain threshold, usually in the range of the grain size. It also states that surface defects are more deleterious. In the absence of significant surface defects, and with internal defects smaller than the grain size, the fatigue life will thus be controlled by the second most prevalent parameter: the microstructure.

Advanced studies on the 316L LPBF microstructure [START_REF] Wang | Additively manufactured hierarchical stainless steels with high strength and ductility[END_REF][START_REF] Wang | Crystallographic-orientation-dependent tensile behaviours of stainless steel 316L fabricated by laser powder bed fusion[END_REF] have shown that excellent strength-ductility combinations could be achieved, depending largely on the crystallographic orientation of the samples, and that it was even possible to surpass the properties obtained with conventional methods. Some results obtained by conventional methods extrapolated at R=0.1 [START_REF] Guerchais | The effect of the microstructure and defects on crack initiation in 316L stainless steel under multiaxial high cycle fatigue[END_REF] show lower fatigue performances, for identical failure mechanisms (microstructure crack initiation). In this study, the prevalent texture was oriented <011> along the loading direction, and comprised cellular sub-grains structures. This specific orientation, along with this fine microstructure, has been observed to accommodate very high deformations, by combining twinning and lattice rotation [START_REF] Wang | Crystallographic-orientation-dependent tensile behaviours of stainless steel 316L fabricated by laser powder bed fusion[END_REF], in addition to some dislocation slip. It also raises the yield strength via a pseudo Hall-Petch effect [START_REF] Wang | Additively manufactured hierarchical stainless steels with high strength and ductility[END_REF], which is known to raise the fatigue life [START_REF] Gerin | Beneficial effect of prestrain due to cold extrusion on the multiaxial fatigue strength of a 27MnCr5 steel[END_REF].

Those results are highly promising for metal additive manufacturing, by showing that the process not only enables higher part complexity, but could also make parts with highly improved fatigue endurance.

Despite parametric optimisation, numerous small pores remained in the samples. A fine 2D metallographic analysis revealed that 97% of those pores had √𝑎𝑟𝑒𝑎 of 10 µm and under, and were thus not observed with X-ray tomography. However, no critical pore of 10 µm or less was ever observed in this study. Among the grains constituting the bulk, only 10% of them had dimensions of 10 µm and under (Figure 3 c)). This observation tends to suggest that the pores need to be larger than most of the surrounding grains to become critical, or else the fatigue life is primarily dictated by the microstructure, as it was observed for most of the optimized samples. Guerchais et al. [START_REF] Guerchais | Micromechanical investigation of the influence of defects in high cycle fatigue[END_REF][START_REF] Guerchais | Effect of defect size and shape on the high-cycle fatigue behavior[END_REF] demonstrated this effect numerically by introducing defects with different sizes and shapes in artificial microstructures using polycrystalline plasticity coupled with probabilistic and deterministic fatigue models. In both cases they observed little impact of the defect on the endurance fatigue limit while the defect root area is below the grain size. It appears that the size threshold at which defects become critical depends mostly on their position: surface or bulk. These sizes measured in √𝑎𝑟𝑒𝑎 are around 20 µm for surface defects, and at least ten times larger (200 µm) for internal defects. This result differs the Murakami criterion [START_REF] Murakami | Metal Fatigue : Effect of Small Defects and Nonmetallic Inclusions[END_REF], which predicts that internal defects should compete with surface defects only 1.7 times larger. Indeed, in this study, artificial internal defects with a √𝑎𝑟𝑒𝑎 of 186 µm (105 µm radius) were not critical for the fatigue life, and the critical crack initiation occurred on surface pores 3 to 7 times smaller. This experimental result confirms the early observations done in previous work [START_REF] Andreau | A competition between the contour and hatching zones on the high cycle fatigue behaviour of a 316L stainless steel: Analyzed using X-ray computed tomography[END_REF] that suggested that internal defects in LPBF 316L are not critical, even with root areas 4 to 10 times larger than the surface defects dimensions.

The distance from the surface at which internal defects become more deleterious has not been identified

clearly in the current study, which suggest a low sensitivity of the material to the reduction of the ligament size. In particular, LPBF-ed 316L seems less impacted by subsurfacic defects than other LPBFed materials, such as an aluminium alloy studied by Bonneric et al. [START_REF] Bonneric | Investigation of the sensitivity of the fatigue resistance to defect position in aluminium alloys obtained by Selective laser melting using arti fi cial defects[END_REF] under similar conditions. This observation is likely to be linked to the deformation tolerance of the material provided by its specific microstructure, and deformation mechanisms.

The slopes in the Kitagawa diagram in Figure 13: Kitagawa diagram for all the characterized samples. The defect size for the microstructural crack initiation was arbitrarily fixed at 0.5 µm (the range of the cell size). When an internal critical defect drives the fatigue properties, the dispersion of the measurements is low, which indicate that they are the primary factor influencing the fatigue endurance, before the microstructure. In turn, the stress concentration induced by the defects is likely to play a role.

Indeed, the internal and critical lack-of-fusion characterized in previous work [START_REF] Andreau | A competition between the contour and hatching zones on the high cycle fatigue behaviour of a 316L stainless steel: Analyzed using X-ray computed tomography[END_REF] but with the same √𝑎𝑟𝑒𝑎 than 430 µm diameter deterministic defects limited the fatigue endurance to 370 MPa, versus 440 MPa in average with deterministic defects. The lacks-of-fusion cluster from previous work lacked symmetry and was highly tortuous, as illustrated in Figure 5 d). The stress concentration induced by its geometry remain however of second importance after its internal position. Indeed, it remains 7 to 8 times larger than the critical surface defects that induced identical fatigue performances.

Some indication as to why the critical pore dimensions are so far apart depending on their location could be found in the fracture surfaces. It can be observed in Figure 11 that the crack propagation surfaces change completely when the crack is connected to the surface of the sample, going from flat to more striated. This change is particularly sharp when a defect is close to the surface, as in Figure 11 c) and d). The major difference that arises when the crack connects to the surface is the environnement. Indeed, the gas in the LPBF fabrication chamber is mostly argon (400 ppm of oxygen maximum). The gas surrounding the powder grains in deterministic pores is thus mostly argon, whereas air surrounds all the surface pores. Figure 14 a) and b) show close up pictures of a crack initiation and propagation occurring from a surface defect and an internal deterministic pore respectively. The rough crack path following surface pore crack initiation shows very few shared grains and consist mostly in intergranular propagation, while intragranular propagation is mostly observed for an internal pore crack initiation. Those observations are in accordance with several works on fatigue cracking in numerous alloys [START_REF] Petit | Influence of ambient atmosphere on fatigue crack growth behaviour of metals[END_REF][START_REF] Grindberg | The effect of vacuum on fatigue crack growth[END_REF][START_REF]Fractography of Fatigue Crack Propagation in 2024-T3 and 7075-T6 Aluminum Alloys in Air and Vacuum[END_REF]. It is stated that air can weaken the grain boundaries, with the action of oxygen [START_REF] Duquette | The effect of environment on the mechanism of stage 1 fatigue fracture[END_REF] or hydrogen [START_REF] Kanezaki | Effects of hydrogen on fatigue crack growth behavior of austenitic stainless steels[END_REF]. The crack propagation could thus be highly impacted, as an intergranular crack propagation through fragilized grain boundaries becomes energetically favourable. On the opposite, argon has no action on the grain boundaries as it is inert, and samples behave like in vacuum.

However, no significant differences in fatigue life were observed between the R430, D430 and M430 sets, despite the cracks that benefited the inert argon atmosphere for various propagation length.

Moreover, in the high cycle fatigue domain (around 10 6 cyles) the crack propagation time usually takes less than 10% of the total life of a fatigue sample [START_REF] Socie | Critical Plane Approaches for Multiaxial Fatigue Damage Assessment[END_REF]. One could still find differences in the early stages of propagation. As the deterministic defects are large, it could be expected that crack initiation occurs early, in multiple locations [START_REF] Morel | Plasticity and damage heterogeneity in fatigue[END_REF]. Only the most favourably oriented of those short cracks will propagate, through the easiest path [START_REF] De Los Rios | Short Crack Fatigue Behaviour in a Medium Carbon Steel[END_REF][START_REF] De Los Rios | a Micro-Mechanics Analysis for Short Fatigue Crack Growth[END_REF]. The first microstructural barrier encountered by a short crack will thus play an important role. In argon, the beginning of intragranular crack propagation will require to shear the next grain the less favourably oriented, and pass over the barrier of the grain boundary (Figure 14 c)). However, with the help of air, intergranular crack propagation can occur at lower stress levels, as the crack will preferentially follow the weakened grain boundary. The stress level necessary to propagate a crack in argon atmosphere being higher than in air, it will require either a larger defect (higher stress concentration) or a higher stress level. For LPBF-ed 316L, a defect can be considered internal and thus be acceptable if it is located a few hundreds of microns under the surface, with dimensions not exceeding 200 microns approximatively. This result is of great importance, as it proves that obtaining a high density material up to roughly 300 µm under the surface, while maintaining an internal defect population with dimensions not exceeding 200 µm should provide excellent fatigue properties. The internal defecttolerance of the LPBF-ed 316L could enable to speed up the manufacturing process with no impact on the fatigue properties. The productivity of the LPBF process is indeed one of the highest challenges in the industrial additive manufacturing world [START_REF] Wohlers | 3D Printing and Additive Manufacturing State of the Industry[END_REF]. In a similar way, the defect control methods for LPBFed 316L should mainly focus on the subsurface, while a lesser resolution and quicker execution should suffice to detect internal deleterious defects.

Conclusions

316L fatigue samples have been manufactured using selective laser melting, using optimized parameters that offered a minimum amount of porosity. Thanks to the shape design freedom of the LPBF process, deterministic submillimetric round pores were generated in the bulk of the samples. Fully dense samples and other samples containing deterministic pores of various sizes and position were then tested in fatigue using a step method. Although the results of this study only apply to LPBF-ed 316L, the deterministic defect generation method could be used to characterize other alloys depending on their relative ductile or brittle behaviour. Several conclusions on the mechanical behaviour of LPBF-ed 316L can be drawn from this work:

• Fully optimized samples showed fatigue strength at 10 6 cycles very close to their maximum strength from tensile tests in the absence of critical pores, contrary to most other LPBF-ed alloys. Microstructural crack initiation was observed and the high mechanical properties can be linked to the fine microstructure of as-built LPBF-ed 316L samples.

• The dimensions at which a defect can become critical in fatigue depend mostly on its position.

Surface pores were found to be far more deleterious than internal ones, with threshold root areas of around 20 µm versus 200 µm for pores under the sample surface. This observation confirms the trends observed in previous work that showed that large internal lacks-of-fusion were less deleterious than 4-10 times smaller surface defects.

• No significant differences were found in fatigue samples with 430 µm defects placed at various distances from the sample surface. Only a 10% increase in fatigue performance has been observed between offcentered and centered defect samples. It is suspected that defect tolerance of the LPBF-ed 316L is attributed to its high ductility, with multiple deformation accommodation mechanisms.

• Fracture surface analysis revealed that the gaseous environment in likely to play an important role on the fatigue life of the samples. As only inert gas surround internal pores, no embrittlement of the grain boundaries can occurs, contrary to surface pores surrounded by air.

The first microstructural barrier before the crack propagation stage is considered to be the largest obstacle to cross. Crack propagation from internal pores is mostly intragranular, which requires higher stress concentration than intergranular crack propagation from surface defects

Aknowledgements

This work was financially supported by the CEA List, the PIMM laboratory, the I2M laboratory and the LAMPA laboratory in France.

Figure 1 :

 1 Figure 1: a) Laser scanning strategy used to melt the powder visualized in the X-Y plane b) Along the fabrication direction

Figure 2 :

 2 Figure 2: a) Small section samples, b) Large section samples (ISO 1099:2017(E)), c) Position and sizes of the deterministic defects in the large samples the size and position of the deterministic defects

Figure 3 :

 3 Figure 3: EBSD mapping of the microstructure visualized along the X axis and taken a) along the fabrication direction and b) on the plane perpendicular to the fabrication direction c) Comparison of the grain and pore size

Figure 4 :

 4 Figure 4: a) Melt pools and corresponding laser parameters sets around a test deterministic pore b) EBSD mapping around a small test deterministic pore according to the laser parameter sets, visualization along the Z-axis.

Figure 5 :

 5 Figure 5: a) b) c) 3D reconstruction and colorization of deterministic pores of different sizes after µ-CT observation. d) Natural lacks-of-fusion observed in previous work [25] e) Powder grains observed inside a deterministic pore.

Figure 6 :

 6 Figure 6: Stress steps applied using the Locati method for the optimized samples

Figure 7 :

 7 Figure 7: Fracture surface with enlarged image of the boxed critical defect for the sample a), b) S-1 and c), d) S-3. √𝑎𝑟𝑒𝑎 of 137 and 23 µm respectively.

Figure 8 :

 8 Figure 8: Crack initiation zones in a) S-6, b) S-5, c) S-4, d) S-7. e), f) Enlarged image in the boxed zones in c) and d) respectively

Figure 9 :

 9 Figure 9: Fracture surface and close-up on the critical defect for a) b) Sample L-4 and c) d) Sample L-2

Figure 10 :

 10 Figure 10: a) C210-1 fracture surface with b) close-up on the critical pore.c) C430-1 fracture surface with d) close-up on the critical (and deterministic) pore. e) C850-3 fracture surface with f) close-up on the critical (and deterministic) pore, g) h)close-up in f) in the boxed zones A and B respectively.

Figure 11 :

 11 Figure 11: Fracture surfaces of samples a) M430-3, b) D430 -3 and c) R430-3. d) close-up picture on the deterministic pore in sample D430-3.

Figure 12 :

 12 Figure 12: Evolution of the maximum stress with the distance between the defect and the surface of the sample

Figure 13 :

 13 Figure 13: Kitagawa diagram for all the characterized samples. The defect size for the microstructural crack initiation was arbitrarily fixed at 0.5 µm (the range of the cell size).

Figure 14 :

 14 Figure 14: a), b) crack initiation and propagation zones for a surface and a deterministic internal pore respectively. c) Schematic illustration of the crack propagation in air and in argon.

1 ) Hatch spacing or distance (µm)

					Number
					of lines
	Hatching	200	800	110	/
	Contour	100	400	70	2
	Downskin hatching	100	1000	60	/
	Downskin contour	100	1250	70	2

Table 1 :

 1 Main laser parameter sets

Table 2 :

 2

Nomenclature and number of the large samples depending on the size and position of the deterministic defects

Table 3 :

 3 Summary of all the fatigue tests carried out. * 10 5 cycles step instead of 10 6 cycles, ** failure during the first cycle of the last step

	End step (MPa)	Number of steps	Cycles last step (x10 5 )	√area defect (µm)	Critical defect
	S-1	1	8.58	137	Surface defect
	S-2	10	4.43	X	Microstructure
	S-3	4	8.59	23	Surface defect
	S-4	9	5.89	X	Microstructure
	S-5	16	2.99	X	Microstructure
	S-6	10	3.50	X	Microstructure
	S-7	10	2.61	X	Microstructure
	L-1	2	7.08	27	Surface defect
	L-2	8	2.31	35	Surface defect
	L-3	6	1.33	46	Surface defect
	L-4	11	4.11	16	Surface defect
	L-5	9	8.62	X	Non observable
	L-6	10	3.66	42	Surface defect
	C210-1	7	5.54	55	Surface defect
	C210-2*	8	7.57	25	Surface defect
	C210-3	8	5.46	31	Surface defect
	C430-1	9	1.66	396	Deterministic
	C430-2	10	3.85	388	Deterministic
	C430-3	8	6.91	387	Deterministic
	C850-1	1	3.98	832	Deterministic
	C850-2	3	5.07	787	Deterministic
	C850-3	4	2.10	819	Deterministic
	C850-4	3	4.37	795	Deterministic
	R430-1	6	5.54	425	Deterministic
	R430-2	7	4.71	426	Deterministic
	R430-3	8	/ **	399	Deterministic
	D430-1	5	6.75	403	Deterministic
	D430-2	6	5.67	432	Deterministic
	D430-3	8	4.28	408	Deterministic


Patrice Raveneau
email: patrice.raveneau@univ-lr.fr

Emmanuel Chaput
email: chaput@enseeiht.fr

Riadh Dhaou
email: dhaou@enseeiht.fr

André-Luc Beylot
email: beylot@enseeiht.fr

A multi-level FREAK DTN: Taking care of disconnected nodes in the IoT

The devices used for such an application have to be cheap since their number would be high. They also have to be energy-efficient; then, it is compulsory to use low energy consuming communications protocols. This constraint implies that a cellular or Wi-Fi network could not be used because consuming too much energy. Protocols such as the IEEE 802.15.4 fit for this situation. Having recourse to this family of protocols implies that the network would suffer from many link disruptions. This is why we focus here on a Disruption Tolerant Network (DTN) for IoT with opportunistic contacts.

In [START_REF] Jung | A link contact duration-based routing protocol in delay-tolerant networks[END_REF], the authors propose a forwarding-based DTN routing protocol named Link Contact Duration-based Routing Protocol (LCD). This solution uses the intercontact duration and the number of messages to determine which messages have to be sent to which relay. LCD achieves good performance but it is compared only to other forwarding-based protocols with one mobility dataset. Maybe some replications-based protocols could achieve better performance. Furthermore, the mobility dataset used for simulations is from a bus network which is predictable in advance with the timetables. That is why, we use several mobility datasets, so that our conclusions do not apply only for one kind of mobility.

As the authors of [START_REF] Nelson | Encounter-based routing in dtns[END_REF] explain, DTN routing protocols can be classified into three categories which are based on forwarding, replication with or without quota. Quota and flooding based protocols are the two sub-categories of replica-based routing protocols. MaxProp [START_REF] Burgess | Maxprop: Routing for vehicle-based disruption-tolerant networks[END_REF] and Prophet [START_REF] Lindgren | Probabilistic Routing Protocol for Intermittently Connected Networks[END_REF] are the most known flooding-based routing protocols while Spray And Wait [START_REF] Spyropoulos | Spray and wait: An efficient routing scheme for intermittently connected mobile networks[END_REF] is a very efficient and simple quota-based routing protocols with a first phase where the replicas are spread among the nodes then a second phase where each replica might only be sent to the destination. Epidemic [START_REF] Vahdat | Epidemic routing for partially-connected ad hoc networks[END_REF] is also a flooding-based protocol where at each contact nodes send to each other every single message that the other node does not have in memory and never carried. Encounter-Based Routing (EBR) [START_REF] Nelson | Encounter-based routing in dtns[END_REF] is a quotabased routing protocol which is very elegant by taking into consideration the past encounters with destinations while not wasting memory resource with unnecessary replicas.

MaxProp, Prophet and EBR provide high performance in a mobile and opportunistic networks but are very complex. Some elegant solutions might be too complex to fit on IoT devices such as WSN430 [START_REF]Hardware wsn430 node[END_REF] with very limited ROM (48 kB) and RAM (10 kB) [START_REF] Raveneau | Experiments and results on DTN for IOT III Urbanet collaboration[END_REF].

Abstract-Crowdsensing is, for a few years, a hot topic. Until now, research on crowdsensing mainly focused on scenarios with devices such as smartphones with huge memory and high computive skills. With the development of the Internet of Things (IoT), crowdsensing can be envisaged with other constraints. Indeed, some IoT nodes are mobile but with limitations about storage and processing capabilities, then connectivity disruptions might occur between the nodes. These issues are tackled by a Disruption Tolerant Networking architecture. In this article, we focus on a subset of IoT, Mobile Sensing Networks (MSN). We propose then, a mechanism which respects the constraints of the nodes and maintains high performance. This mechanism, the multi-level FREAK, uses the mean frequency of contacts with the destination. The metrics drives the transmission. Since some nodes might not meet the destination nor nodes meeting the destination, we had the idea of a multi-level metrics to allow these "disconnected" nodes to transmit data to the destination. We evaluate our proposal through simulations based on several real mobility traces. Our solution outperforms reference replication and quota-based DTN solutions.

Index Terms-Internet of Things, Disruption Tolerant Networking, Opportunistic network, Data transmission.

I. INTRODUCTION

The interest for the Internet of Things (IoT) has been growing in the last few years. Cisco forecasts that the IoT will generate $19 trillion over the next decade [START_REF]The internet of everything is the new economy[END_REF]. The spectrum of applications which can benefit from IoT is very large. Indeed, these applications go from personal private uses to urban and smart cities purposes [START_REF] Gomez | Urban automation networks: current and emerging solutions for sensed data collection and actuation in smart cities[END_REF].

With IoT for a personal usage, people can follow metrics such as how many steps they have accomplished along the day or if their potted plants require more water. In a smart city context, the applications might use static sensing nodes with smart metering or air pollution monitoring [START_REF] Boubrima | Optimal deployment of wireless sensor networks for air pollution monitoring[END_REF].

Nevertheless, when talking about static IoT nodes, it is compulsory to analyse before deployment the limits of the network to sense this data in order to optimize the placement of nodes. Mobile IoT does not suffer from this constraint. Considering an air pollution monitoring scenario, it is possible to collect data measurements with mobile sensors which would be installed on city bus or on bikes of a bicycle-sharing system. A system combining sensors from buses and from bikes would allow to take measurements from several patterns with buses and measurements from other locations thanks to the bikes.

Most DTN studies focus on peer-to-peer communications meaning the data exchanged in the network goes from random sources to random destinations. These settings allow to model communications to exchange data between entities in the network such as text messages between two humans or pieces of a navigation map within a vehicular network. Nevertheless, when considering crowdsensing, the main goal is to be able to retrieve data from the sensing nodes to a gathering machine whose aim is to store data. In the specific case of crowdsensing with IoT, the energy constraint limits the ability of nodes to communicate with an infrastructure network. We consider that one or few nodes of the mobile sensing network serves as gateway between mobile IoT nodes and an infrastructure network able to communicate with the storing server.

This paper is organised as follows. We present in a first time the proposed mechanism in section II then we describe the tools and datasets we used to evaluate our proposal in section III before analysing the results of the simulations in section IV and finally we conclude on what we learned from this study in section V.

II. WHERE THE MULTI-LEVEL FREAK COMES FROM

One of the most important limitation of the context of this study is the low memory and computation skills of the devices intended to be used in mobile sensing IoT. Because of this hardware constraint most smart DTN solutions cannot be implemented on the nodes. We use for comparison some of the best mainstream DTN routing protocols but we have to keep in mind that the algorithms used by these solutions are too greedy with resources. The comparison allows us to check if our proposal performs well compared to solutions requiring a lot more resource to work.

As the authors of [START_REF] Nelson | Encounter-based routing in dtns[END_REF] claim, it might be possible to infer future encounters based on the ones that occured in the past. The FREAK solution, whose main idea is that only the frequency of encounters with the set of destinations matters, appears to be a good option. Nonetheless, we have to take into consideration the fact that nodes might have a mobility pattern which leaves them too far from the destination; and even too far from nodes close to the destination. A simple example would be a scenario where two nodes N and M never meet the destination D and where a third node L would meet the destination. N never meets L, but M does. With the FREAK solution, N shall not send to M because its value of the metric is bad as the one of N. But since M can forward data to L which meets the destination, N should transmit data to M to reach the destination.

That is why, we inspired from the results on κ-vicinity from [START_REF] Tatar | Beyond contact predictions in mobile opportunistic networks[END_REF] to extend the simple FREAK solution [START_REF] Raveneau | Freak dtn: Frequency routing, encounters and keenness for dtn[END_REF] in a mechanism which would take benefit from multi-hop contacts. With this solution, that we named multi-level FREAK (ML-FREAK) DTN, we should be able to decrease problems like described earlier, that might occur in some networks. Now that we explained the motivations to propose our ML-FREAK solution, we describe the behaviour of the protocol. Before the transmission of any data packet (named Bundles when using the DTN Bundle Protocol [START_REF] Scott | Bundle Protocol Specification[END_REF]), when two nodes meet, they exchange their values of the metrics. We use an array of frequencies with groups. The first value of the array is the frequency of encounters between the node and the set of destinations. The second value is the frequency of encounters between the node and a set of nodes meeting the destination; and so on. We limited to an array of eight values in order to limit the impact on the memory of the nodes. Furthermore, we believe that given a network not exceeding the size of a city, eight hops is enough to cover the whole area.

Once the nodes exchanged their vector of metrics, they run the algorithm 1 to update their vector and make a decision on whether sending replicas of messages they carry or not.

Algorithm 1 Multi-level FREAK Transmission Decision

Let A be the local node while true do for all met node (named B) do if B is the destination then

nbrContacts[0] + + f req[0] = nbrContacts[0] CurrentT ime
Send all Bundles Remove all delivered Bundles else i = 1 while (i < 8)and(f

req[i](A) == 0)and(f req[i -1](B) == 0) do i + + end while if (i < 8) then nbrContacts[i] + + f req[i] = nbrContacts[i] CurrentT ime end if i = 0 while (i < 8)and(f req[i](A) > f req[i](B)) do i + + end while if (i < 8)

III. EVALUATION ENVIRONMENT

Our evaluation is realised through simulations with the DTN simulator The ONE [START_REF] Keränen | The ONE Simulator for DTN Protocol Evaluation[END_REF]. This simulator does not take into account problems from the MAC layer assuming that any problem of this level would be tackled by a protocol from this level. Our goal is to compare the ML-FREAK to the simple one and to analyse if its performance is close to performance from more complex and unimplementable DTN routing protocols.

We use several mobility traces for our simulations in order to limit the importance of the mobility patterns of one trace in a specific context. We present first these datasets and analyse their differences and similarities. Thanks to this analysis we can check if some mobility characteristics might have an influence on network performance.

A. Datasets presentation

We gathered several mobility traces and contact traces from the CRAWDAD website then used the Adyton tool [START_REF] Papanikos | CRAWDAD toolset tools/simulate/uoi/adyton (v. 2016-04-21)[END_REF] to generate contact traces for each trace that we selected. The Adyton tool provides a DTN simulator we found less powerful in terms of settings compared to The ONE. Then we modified our contact traces in a format compatible with The ONE.

The traces that we used were collected at conferences such as Infocom05 (Inf5), Infocom06 (Inf6), Sigcomm09 (Sig9). This type of traces are very specific because the public is attending an event. We also used traces coming from campuses such as the MIT Reality (MIT) and Milano (Milano). Finally, we used the Cambridge (Camb) and DieselNet (DN), collected at a city level for the former and thanks to a DTN installed on buses of UMass Amherst campus for the latter.

We realise an analysis on the number of contacts that each node makes during the whole simulations. We will not compare the extreme values of each dataset for the number of contacts since as we can see on Table I the durations of simulations are not in the same range. We analyse the trends of the distributions thanks to boxplots presented in Figure 1.

From this figure, we note that the shorter a scenario is and the closer are the quartiles of the number of contacts per node. Indeed, the four traces with the smallest durations (Camb, Inf5, Inf6 and Sig9) are the ones with the tightest boxplots while the three others which last a lot more in time present loose boxplots. This trend is not impacted by the number of nodes. This can be explained by the fact that on small periods people will have very similar mobility patterns (going to work, getting home, etc.); while once the duration of the mobility trace is longer than a few weeks the mobility patterns start to diverge. Then for the three other traces, nodes do not move in the same manner and this can explain why the whiskers are bigger.

The mean, represented with diamonds, is most of the time close to the median meaning the distribution of number of contacts per node is uniform. For Milano and MIT datasets where the mean is between the median and the third quartile, there are more nodes having a lot of contacts than nodes having very few contacts.

We analysed the number of contacts per node since contacts are a key element for opportunistic networks. We also analyse on Figure 2 for each dataset. On this figure we indicated the maximum value of the intercontact duration at the end of the top whisker because some values were too high to get a clear interpretation.

We see that there is no strong correlation between the distributions of number of contacts and inter-contacts durations. Indeed, we note a strong correlation between the three conferences datasets with low inter-contacts durations, that we can explain because of the small covered area. The distribution of inter-contacts of the bus network has very low quartiles with maximum and mean values far upper from the third quartile, as are the distributions for Camb, Milano and MIT.

From this analysis, we think that the performance results of our simulations run on conferences datasets might be very specific because the mobility and contacts look like they are very different to the other mobility traces. The four other traces which do not share an identical scenario have nonetheless similar statistics on the metrics we analysed.

B. Simulations parameters

We focus on a scenario of IoT crowdsensing with cheap devices. We assume that the measurements are made periodically every hour. We do not take into account applicative mechanisms that would decide to not transmit a measurement because the value is the same as the previous one. We make this assumption because we want to know the performance of a network with a given load. If some mechanisms allow to decrease the load, then the network should perform even better. We consider one scenario with one destination and we select three different destinations based on the analysis of the number of contacts of each node. The first run is when the node having the highest number of contacts is selected as destination. The second run is with a destination selected within the nodes having the smallest number of contacts. And the third run is with the destination randomly picked among nodes having a number of contacts close to the first quartile. By varying the type of destinations, we want to analyse if it is better to have a node with a lot of encounters as a destination or as a relay.

We summarize the simulations settings in Table II. We consider that for applications whose aim is to monitor the environment, a periodic measurement with a period of one hour allows to get an accurate information on the measured metrics. Since this data is not critical, the delay to collect it is not limiting. Then we choose time to live (TTL) values high and we vary the TTL between 12 and 60 hours.

We compare the ML-FREAK mechanism to DirectDelivery (DD) where nodes transmit only to the destination, EBR, Epidemic, the simple FREAK scheme, MaxProp, Prophet and SprayAndWait (SAndW).

IV. RESULTS INTERPRETATION

Now we analyse the results of our simulations. First of all, we will not use figures for the results when the destination is either a node with the least number of contacts or with a number of contacts close to the first quartile of the dataset. Indeed, for these settings, the delivery ratio was around one or two percents for every routing protocol on each dataset.

From these results, we can conclude that it is far better for a network when the destination is a node making a lot of contacts. We could think that a relay node making a lot of encounters would allow the network to have high performance; but because of the limited storage of the nodes, the performance drops when the destination does not belong to the nodes making the greatest number of encounters.

After this first analysis, we focus on the delivery ratio when the TTL is 12 hours on Figure 3.

The first fact that we note on this figure is that the ML-FREAK scheme provides always better performance than the simple version. This indicates that with the simple version, there are contacts between nodes which are not used. This is now tackled by the multi-level version. We also note that the ML-FREAK provides delivery ratio very close to mainstream DTN routing protocols such as MaxProp and Prophet unless for the conferences scenario. We identified in the analysis on the datasets that the conferences traces had a specific mobility pattern, and this type of mobility is not convenient for low computation solutions. This trend is the same when we increase the TTL of the Bundles to 60 hours. The ML-FREAK is always better than the simple FREAK, but when it is used at a conference, the performance is not at the same level as other mainstream DTN routing protocols. By considering the four other mobility scenarios, the ML-FREAK provides delivery ratio in the same range of solutions like MaxProp of Prophet while our proposal is far less complex than these two solutions. On the trace coming from Milano, our solution is even better than EBR which is also more complex than ML-FREAK.

With Figures 5 and6, we note one of the drawback of the dropping policy we selected. When a node receives data from a neighbour node and its memory is full, then it drops the messages that it had in memory to be able to get the new messages. This tends to increase the overhead, defined as the number of exchanged messages over the number of delivered ones. Since the ML-FREAK does not order the messages to send in a smart way as MaxProp does, then the delivered messages have a higher probability of coming from nodes which are further (in terms of hops) from the destination. This tends to increase the delay of the delivered messages.

Except with the conferences traces which are maybe biased, ML-FREAK outperforms DTN routing protocols by providing a delivery ratio equal or greater than this from the mainstream DTN routing protocols at a lower computation cost. V. CONCLUSION To conclude this study, we proposed the multi-level FREAK protocol which can fit on small devices with low memory and computation skills and provides a performance level as high as the one of far more complex routing solutions. We also analysed some characteristics on the contacts of several reference mobility datasets and we could determine why some protocols have better performance than others when the mobility scenario is very specific.

As a perspective, we are currently implementing ML-FREAK on real devices (WSN430) and we will test the performance in real conditions. We also envisage to focus on a dropping policy and on an algorithm which would allow to improve the fairness among the sources of messages.

Fig. 1 .

 1 Fig. 1. Comparison of distributions of number of Contacts per mobility dataset

Fig. 3 .

 3 Fig. 3. Delivery Ratio with TTL = 12h

Fig. 4 .

 4 Fig. 4. Delivery Ratio with TTL = 60h

Fig. 5 .Fig. 6 .

 56 Fig. 5. Overhead ratio with TTL = 60h

  the distribution of inter-contacts duration per node

			3095 3649			2150 38365
		2000
	Intercontacts Durations	500 1000 1500		487
					331	284
		0
			Camb DN	Inf5	Inf6 Milano MIT Sig9
					Trace
	Fig. 2. Comparison of distributions of inter-contacts durations per mobility
	dataset
				TABLE I
		IMPORTANT VALUES OF MOBILITY TRACES
	Traces		mean(s)	max(s)	# nodes	Duration (s)
			intercontact	intercontact
	Camb [17]	1,846	588,020	54	987,529
	DN [18]	2,659	879,7164	37	10,635,474
	Inf5 [17]	213	182,542	41	254,150
	Inf6 [17]	102	65,337	98	337,418
	Milano [19]	2,385	84,0503	49	1,632,979
	MIT [20]	9,444	5,673,540	97	24,428,517
	Sig9 [18]	182	158,400	76	320,774