The Effect of Microstructural Defects on High-Cycle Fatigue of Ti Grade 2 Manufactured by PBF-LB and Hydrostatic Extrusion

: The aim of this study was to show the effect of manufacturing defects in a commercially pure Ti Grade 2 produced by a laser beam powder bed fusion (PBF-LB) process on its high-cycle fatigue life. For this purpose, the high-cycle fatigue performance of PBF-LB Ti Grade 2 was compared to its ultrafine-grained (UFG) counterpart processed by hydrostatic extrusion exhibiting a similar mechanical properties under static tensile. The yield strength of the PBF-LB and UFG Ti Grade 2 was 740 and 783 MPa, respectively. The PBF-LB Ti Grade 2 consisted of a typical columnar of prior β grains with an acicular martensite α ’ microstructure, while UFG Ti Grade 2 was mainly composed of fine, equiaxed α phase grains/subgrains with a size of 50–150 nm. A residual porosity of 0.21% was observed in the PBF-LB Ti Grade 2 by X-ray computed tomography, and, despite similar yield strength, a significantly higher endurance fatigue limit was noticed for UFG Ti Grade 2 (420 MPa) compared to PBF-LB Ti Grade 2 (330 MPa). Fatigue striation analysis showed that the fatigue crack propagation rate was not affected by manufacturing technology. In turn, the high-cycle fatigue life was drastically reduced as the size of manufacturing defects (such as pores or lack of fusion zones) increased.


Introduction
Additive manufacturing (AM) techniques have become very promising fabrication processes that enable the production of near fully dense 3D metal parts with a complex geometry in a single fabrication step [1,2]. Due to the limitations of the processing stages and the possibility of near net shape production of metallic elements, AM technology is a perfect solution for difficult-to-manufacture materials, such as titanium and titanium alloys [3,4]. A laser beam powder bed fusion (PBF-LB) process has been widely used in recent years for the fabrication of elements made of a commercially pure (CP) Ti Grade 2 [5][6][7][8] or Ti-6Al-4V alloy [3,4]. It involves melting thin metallic powder layers by a laser beam to build 3D parts in a layer-wise manner [9]. Such Ti-based 3D products with a controlled geometry combine a high specific strength with excellent biocompatibility and corrosion resistance, and this makes them extraordinary candidates for many biomedical applications in the fields of orthopedics and dental implantology [3,10]. Unfortunately, manufacturing defects are an unavoidable characteristic of AM metal structures, including porosity, unmelted particles, and a lack-of-fusion zones, which lose their fracture toughness and fatigue under cyclic loading, thereby limiting their further usage in load-bearing applications [11]. 2 of 14 The fatigue behavior of AM products is mainly controlled by the abovementioned manufacturing defects, surface roughness, and residual stresses [11,12]. In general, the as-built AM components possess a high value of residual stresses [13]. As shown by Rans et al. [14] and Leuders et al. [15] for the Ti-6Al-4V alloy, such residual stresses strongly affect fatigue crack growth behavior and increase the crack growth rate in the as-built specimens to a level higher than for a wrought material. Nevertheless, the residual stresses can be reduced by preheating a building platform [16] or by post-processing heat treatment [15,17]. The effect of the as-built surface roughness on the fatigue life of AM Ti-6Al-4V alloy has been investigated by Vayssette et al. [18] and Wycisk et al. [19], and these two studies reported a significant enhancement of fatigue strength after machining (or additional polishing). The endurance fatigue limit of the as-built samples was of about 210-220 MPa, whereas a proper surface finish caused an increase in fatigue strength up to a level of 500-510 MPa [18,19]. This shows the necessity of machining and removing possible stress concentration sites before cyclic loading of the additively manufactured structures. However, the fatigue resistance of the laser beam fabricated components seems to be mostly related to the intrinsic manufacturing defects, which can be categorized as gas porosities, unmelted particles, and lack-of-fusion zones [12]. Some of the crack initiation sites are identified as spherical porosities that are caused by a trapped gas in the powder material [12,20], but the majority of the cracks are generated at lack-of-fusion zones and by unmelted particles [21][22][23]. Liu et al. [21] showed for the as-built Ti-6Al-4V specimens that the fatigue cracks were primarily initiated at the lack-of-fusion zones, and that the location, the size, and the shape of these zones determined the reduction of the fatigue life. The detrimental effect of the lack-of-fusion zones was also confirmed by Walker et al. [22] and Chastand et al. [23] in their studies.
In order to expand the usage of the additively manufactured Ti-based materials in the biomedical field, their fatigue performance has to be improved. It has been shown that the fatigue life of additively manufactured Ti-based materials is mainly affected by surface roughness, residual stresses, or manufacturing defects. The first two can be mitigated by a combination of preheating, post-processing heat treatment, and an accurate surface finish by machining and polishing, while the last one seems to be unavoidable. Even a hot isostatic pressing (HIP) of the as-built products is not able to entirely reduce internal defects [23]. Therefore, the aim of this study was to show the strength of the effect of manufacturing defects in the CP Ti Grade 2 produced by the PBF-LB process on its high-cycle fatigue life. For this purpose, the high-cycle fatigue performance of PBF-LB Ti Grade 2 was compared to its ultrafine-grained (UFG) counterpart processed by hydrostatic extrusion (HE), which exhibited similar mechanical properties under static tensile. It is commonly accepted that the fatigue strength in the high-cycle fatigue (HCF) regime is proportional to the yield strength [24,25]. Thus, the PBF-LB and UFG Ti Grade 2 should theoretically exhibit comparable high-cycle fatigue limit. To reduce the influence of surface roughness and residual stresses, PBF-LB Ti Grade 2 was manufactured at a preheated building platform, stress relieved by annealing at 400 • C for 4 h, and precisely machined and polished before fatigue tests. PBF-LB and UFG Ti Grade 2 were characterized in terms of microstructure, porosity, tensile and fatigue properties, and fatigue crack growth resistance based on a fatigue striations spacing analysis. Ti Grade 2 was analyzed in this study because it can be a good alternative to less biocompatible Ti alloys (e.g., Ti-6Al-4V), especially in the field of dental and maxillofacial implantology [26,27]. Moreover, the majority of the data in the literature regarding the fatigue behavior of the additively manufactured materials is related to Ti-6Al-4V alloy, whereas CP Ti Grade 2 is rather scarcely reported.

Materials and Methods
PBF-LB specimens were fabricated from a spherical Ti Grade 2 powder (TLS Technik, Germany) with a particle size range of 15-45 µm (D 10 = 14.7 µm, D 50 = 30.6 µm; D 90 = 44.2 µm). Cylindrical rods with a diameter of 6 mm and a length of 65 mm were additively manufactured in the PBF-LB process using a Realizer SLM50 machine (Realizer GmbH, Borchen, Germany). Cylinders were positioned on a building platform at an angle of 30 • due to the limitations of the building area (as presented in Figure 1). Specimens were fabricated on a titanium substrate preheated to 200 • C. A laser power of 45W, a scanning speed of 325 mm/s (40 µs exposure time and 20 µm point distance between each next point), and a layer thickness of 25 µm were used along with a checkerboard scanning strategy. These laser scanning parameters gave a summarized energy density of approximately 130 J/mm 3 , and they were used to create fully dense titanium parts based on our previous studies [28,29]. A detailed explanation of the optimization methodology for the fabrication of titanium parts using the PBF-LB process is provided in [30]. The laser pattern utilized in this study involved a 5 × 5 mm checkerboard zone with alternating laser scanning and a 90 • rotation for every opposite checkerboard zone, as described in more detail in [31]. An inert argon atmosphere was maintained throughout the PBF-LB process. Before removal from the building platform, the cylinders were placed in a chamber furnace and heat treated at 400 • C for 4 h in an argon atmosphere in order to relieve any residual stresses. Once stress relieving was completed, a conventional machining was used to remove the supports and shape the samples to the desired dimensions for mechanical tests.

Materials and Methods
PBF-LB specimens were fabricated from a spherical Ti Grade 2 powder (TLS Technik, Germany) with a particle size range of 15-45 µm (D10 = 14.7 µm, D50 = 30.6 µm; D90 = 44.2 µm). Cylindrical rods with a diameter of 6 mm and a length of 65 mm were additively manufactured in the PBF-LB process using a Realizer SLM50 machine (Realizer GmbH, Borchen, Germany). Cylinders were positioned on a building platform at an angle of 30° due to the limitations of the building area (as presented in Figure 1). Specimens were fabricated on a titanium substrate preheated to 200 °C. A laser power of 45W, a scanning speed of 325 mm/s (40 µs exposure time and 20 µm point distance between each next point), and a layer thickness of 25 µm were used along with a checkerboard scanning strategy. These laser scanning parameters gave a summarized energy density of approximately 130 J/mm 3 , and they were used to create fully dense titanium parts based on our previous studies [28,29]. A detailed explanation of the optimization methodology for the fabrication of titanium parts using the PBF-LB process is provided in [30]. The laser pattern utilized in this study involved a 5 × 5 mm checkerboard zone with alternating laser scanning and a 90° rotation for every opposite checkerboard zone, as described in more detail in [31]. An inert argon atmosphere was maintained throughout the PBF-LB process. Before removal from the building platform, the cylinders were placed in a chamber furnace and heat treated at 400 °C for 4 h in an argon atmosphere in order to relieve any residual stresses. Once stress relieving was completed, a conventional machining was used to remove the supports and shape the samples to the desired dimensions for mechanical tests. To obtain UFG specimens, a commercially available Ti Grade 2 (0.17% Fe, 0.018% C, 0.009% N, 0.001% H, 0.15% O, Ti balanced) in the form of a rod with an initial diameter of 50 mm was subjected to room temperature HE in two stages: (1) from 50 to 25 mm, and (2) from 25 to 16 mm, resulting in a total accumulated true strain of ε = 2.28. The details of the HE processing can be found in [32].
The microstructure of PBF-LB and UFG Ti Grade 2 was examined with a Zeiss Axio Scope (Carl Zeiss Microscopy GmbH, Kelsterbach, Germany) light microscope (LM) and a JEOL JEM-1200EX (JEOL Ltd., Tokyo, Japan) transmission electron microscope (TEM), respectively. PBF-LB specimens for metallographic observations were ground, polished, and etched with a solution of 25 mL distilled water, 15 mL HNO3, 15 mL HF, and 45 mL HCl. Thin foils for TEM investigation were prepared by cutting 3 mm diameter discs from a cross-section of hydrostatically extruded rods, which were subsequently ground and electropolished. Based on LM and TEM images, a grain size (described by an equivalent diameter d2) was calculated using MicroMeter software (v0.86b) [33]. Additionally, to To obtain UFG specimens, a commercially available Ti Grade 2 (0.17% Fe, 0.018% C, 0.009% N, 0.001% H, 0.15% O, Ti balanced) in the form of a rod with an initial diameter of 50 mm was subjected to room temperature HE in two stages: (1) from 50 to 25 mm, and (2) from 25 to 16 mm, resulting in a total accumulated true strain of ε = 2.28. The details of the HE processing can be found in [32].
The microstructure of PBF-LB and UFG Ti Grade 2 was examined with a Zeiss Axio Scope (Carl Zeiss Microscopy GmbH, Kelsterbach, Germany) light microscope (LM) and a JEOL JEM-1200EX (JEOL Ltd., Tokyo, Japan) transmission electron microscope (TEM), respectively. PBF-LB specimens for metallographic observations were ground, polished, and etched with a solution of 25 mL distilled water, 15 mL HNO 3 , 15 mL HF, and 45 mL HCl. Thin foils for TEM investigation were prepared by cutting 3 mm diameter discs from a cross-section of hydrostatically extruded rods, which were subsequently ground and electropolished. Based on LM and TEM images, a grain size (described by an equivalent diameter d 2 ) was calculated using MicroMeter software (v0.86b) [33]. Additionally, to determine a residual porosity of PBF-LB specimens, X-ray computed tomography (XCT) measurements were performed using a Bruker SkyScan 2011 (Bruker Corporation, Billerica, USA) microtomograph. The obtained data were processed with dedicated CTAn software (v1.14).
Uniaxial tensile and high-cycle fatigue tests were conducted on an MTS 858 (MTS Systems Corporation, Eden Prairie, USA) hydraulic testing machine equipped with a 25 kN load cell. Cylindrical test specimens (presented in Figure 1) were machined from the stress-relieved PBF-LB cylinders and the as-extruded UFG Ti Grade 2 rods. The tensile tests were performed according to the ISO 6892-1 standard at a constant strain rate of 10 −3 s −1 . The high-cycle fatigue tests were conducted according to a ASTM E466 standard in a stresscontrolled mode at a constant frequency of 20 Hz and a stress ratio of R = −1. Before testing, the gage sections were polished using a 3 and 1 µm diamond suspensions to minimize the effects of surface irregularities and remove all of the scratches after machining. Finally, the fracture surfaces were observed using a Hitachi SU8000 (Hitachi Ltd., Tokyo, Japan) scanning electron microscope (SEM) to locate fatigue crack initiation sites and precisely analyze the spacings of the fatigue striations.

Results and Discussion
3.1. Microstructure and Tensile Properties of PBF-LB and UFG Ti Grade 2 Figure 2a,b shows the microstructure of PBF-LB Ti Grade 2 in two mutually perpendicular planes, XY and XZ. It consisted of columnar prior-β grains with a width of 75 ± 10 µm, which grow along the building direction (Z axis) across many deposited layers as a consequence of directional solidification and thermal gradients during the PBF-LB process. Such columnar architecture is a typical microstructural feature for the additively manufactured materials [8,34,35]. Each columnar grain comprised an acicular martensitic α' microstructure, which is consistent with the other reports in the literature. Gu et al. [5] and Attar et al. [6] showed that the martensitic α' microstructure can be obtained in the CP Ti at a laser scanning speed above 100 mm/s (325 mm/s was applied within the current work), while a lower scanning speed results in the formation of plate-like α grains. In general, laser beam fabrication processes lead to extremely high heating/cooling rates (10 3 -10 8 K/s) during heat conduction from the molten powder to the building platform [5,6]. A high laser scanning speed (>100 mm/s) produces high temperature gradients, which, in turn, promote the development of non-equilibrium phases, such as the martensitic α' phase. At lower scanning speeds (<100 mm/s), the thermal accumulation within the molten pool is higher and the effect of quenching that occurs by heat conduction through the substrate is not so effective, which enables a complete transformation of the β to α phase [5,6]. The microstructural observations also revealed a presence of spherical pores and some lack-offusion zones, which are unavoidable manufacturing defects in the additively manufactured materials [3,4]. XCT measurements showed that the porosity was at a level of 0.21% and the observed pores had a size ranging from around 5 to 120 µm (the average pore size was 25.5 µm), as presented in Figure 2c. The pores with a near-spherical shape were mainly gas pores, while the lack-of-fusion zones exhibited irregular or elongated shapes. The microstructure of UFG Ti Grade 2 is presented in Figure 3, and it was mainly composed of fine, equiaxed α phase grains/subgrains with a size of 50-150 nm (the average grain/subgrain size was 102 ± 49 nm) and a small fraction of relatively coarse grains (with a size of several hundred nanometers) with a high density of tangled dislocations or non-fully developed dislocation cells. The selected area electron diffraction (SAED) patterns taken from the TEM images (Figure 3a) also proved to be a development of the UFG microstructure, i.e., diffraction spots formed a relatively continuous circles, which indicate The microstructure of UFG Ti Grade 2 is presented in Figure 3, and it was mainly composed of fine, equiaxed α phase grains/subgrains with a size of 50-150 nm (the average grain/subgrain size was 102 ± 49 nm) and a small fraction of relatively coarse grains (with a size of several hundred nanometers) with a high density of tangled dislocations or non-fully developed dislocation cells. The selected area electron diffraction (SAED) patterns taken from the TEM images (Figure 3a) also proved to be a development of the UFG microstructure, i.e., diffraction spots formed a relatively continuous circles, which indicate high misorientation between the numerous fine grains. These microstructural characteristics of UFG Ti Grade 2 are consistent with the typical microstructures observed for Ti Grade 2 after HE to a similar accumulated true strain [32,36,37]. The microstructure of UFG Ti Grade 2 is presented in Figure 3, and it was mainly composed of fine, equiaxed α phase grains/subgrains with a size of 50-150 nm (the average grain/subgrain size was 102 ± 49 nm) and a small fraction of relatively coarse grains (with a size of several hundred nanometers) with a high density of tangled dislocations or non-fully developed dislocation cells. The selected area electron diffraction (SAED) patterns taken from the TEM images (Figure 3a) also proved to be a development of the UFG microstructure, i.e., diffraction spots formed a relatively continuous circles, which indicate high misorientation between the numerous fine grains. These microstructural characteristics of UFG Ti Grade 2 are consistent with the typical microstructures observed for Ti Grade 2 after HE to a similar accumulated true strain [32,36,37]. The martensitic α' microstructure of PBF-LB Ti Grade 2 and the highly refined α phase microstructure of UFG Ti Grade 2 resulted in their extraordinary tensile properties, which are not commonly achieved for conventionally manufactured CP Ti [24,36]. The estimated tensile properties of PBF-LB and UFG Ti Grade 2, i.e., 0.2% offset yield strength (YS), ultimate tensile strength (UTS), and elongation to failure (A), are summarized in Table 1. PBF-LB Ti Grade 2 exhibited YS = 740 ± 7 MPa, UTS = 866 ± 6 MPa, and A = 29.9 ± 2.2%, while UFG Ti Grade 2 was characterized by the similar tensile properties: YS = 783 ± 8 MPa, UTS = 888 ± 7 MPa, and A = 11.5 ± 0.8%. These strength values were superior to the commonly observed properties for Ti Grade 2 that were processed by conventional extrusion (YS = 440 MPa, UTS = 550 MPa, A = 24% [36]) or cold rolling (YS = 380 MPa, UTS = 460 MPa, A = 26% [24]). UFG Ti Grade 2 processed by HE in this work was even tougher than a severely cold-rolled Ti Grade 2 down to 90%, which corresponded with the same accumulated true strain ε = 2.3 (YS = 600 MPa, UTS = 798 MPa, A = 16% [38]). Moreover, The martensitic α' microstructure of PBF-LB Ti Grade 2 and the highly refined α phase microstructure of UFG Ti Grade 2 resulted in their extraordinary tensile properties, which are not commonly achieved for conventionally manufactured CP Ti [24,36]. The estimated tensile properties of PBF-LB and UFG Ti Grade 2, i.e., 0.2% offset yield strength (YS), ultimate tensile strength (UTS), and elongation to failure (A), are summarized in Table 1. PBF-LB Ti Grade 2 exhibited YS = 740 ± 7 MPa, UTS = 866 ± 6 MPa, and A = 29.9 ± 2.2%, while UFG Ti Grade 2 was characterized by the similar tensile properties: YS = 783 ± 8 MPa, UTS = 888 ± 7 MPa, and A = 11.5 ± 0.8%. These strength values were superior to the commonly observed properties for Ti Grade 2 that were processed by conventional extrusion (YS = 440 MPa, UTS = 550 MPa, A = 24% [36]) or cold rolling (YS = 380 MPa, UTS = 460 MPa, A = 26% [24]). UFG Ti Grade 2 processed by HE in this work was even tougher than a severely cold-rolled Ti Grade 2 down to 90%, which corresponded with the same accumulated true strain ε = 2.3 (YS = 600 MPa, UTS = 798 MPa, A = 16% [38]). Moreover, the obtained YS and UTS for PBF-LB Ti Grade 2 were also slightly higher than those reported for other additively manufactured Ti Grade 2, showing YS and UTS mostly in the range of 520-670 MPa and 610-760 MPa, respectively (Table 1). This can be attributed to the building orientation applied in this work, i.e., PBF-LB Ti Grade 2 specimens were positioned at an angle of 30 • to the building platform. As shown by Ren et al. [39], the higher strength can be achieved at building angles of 30-60 • compared to 0 • (horizontally) and 90 • (vertically) oriented samples, and this is strictly related to differences in the distribution of pores, residual stresses, and crystallographic texture. Ren et al. [39] also noted that specimens built at the angle of 0 • and 90 • possessed the largest gradient of residual stresses and the most potential crack-sensitive areas. This showed that vertical (90 • ) orientation favors cracking at interlayer pores or lack of fusion zones, whereas a wide area of each deposited layer in the horizontal (0 • ) samples caused the temperature gradient between the ends and the sample center to be relatively high, and the intermediate areas between the compressive stresses in the middle part and the tensile stresses at both ends are thus very crack-sensitive. Specimens build at the angle of 90 • also exhibited lower strength due to the higher amount of grains with a "soft" crystallographic orientation, i.e., those characterized by a high Schmid factor of basal <a> and prismatic <a> slip systems, Crystals 2023, 13, 1250 6 of 14 which dominate in the α phase Ti during plastic deformation at room temperature [39]. Nevertheless, most importantly for this study, the YS and UTS of the investigated PBF-LB Ti Grade 2 and UFG Ti Grade 2 were very close to each other, which suggests that these materials may show a comparable high-cycle fatigue strength.

High-Cycle Fatigue Life and Crack Initiation Sites for the PBF-LB and UFG Ti Grade 2
The high-cycle fatigue performance of PBF-LB and UFG Ti Grade 2 is presented in the Figure 4 in the form of a Wöhler plot (S-N curve) representing the stress amplitude (σ a ) versus the number of cycles to failure (N f ). Despite having a similar yield strength, a significantly higher fatigue strength was noticed for UFG Ti Grade 2 compared to PBF-LB Ti Grade 2--i.e., the S-N curve for UFG Ti Grade 2 was shifted to higher stress amplitudes of 420-500 MPa (vs 320-400 MPa for PBF-LB Ti Grade 2) for the corresponding fatigue lifetime. The endurance fatigue limit (on the basis of 2 × 10 6 cycles) reached a value of 420 and 330 MPa for UFG and PBF-LB Ti Grade 2, respectively.
After the high-cycle fatigue tests, the crack initiation sites were analyzed based on SEM observations, as presented in Figure 5. In the case of UFG Ti Grade 2, the fatigue cracks initiated at the surface defects, such as micro-scratches (Figure 5a), which is commonly observed for metallic materials in the high-cycle fatigue regime [24,43]. In turn, the typical fatigue crack initiation sites in the additively manufactured materials are related to the as-built roughness of the surface, internal or sub-surface pores, and the lack-of-fusion zones [12,[21][22][23]. Fractographic observations in the current study showed that the fatigue cracks in the PBF-LB Ti Grade 2 were mostly generated at the sub-surface lack-of-fusion zones (Figure 5b,c,e,f) or residual porosity near the surface (Figure 5d). It has been shown that the defect size and the geometry strongly affect the fatigue strength of metallic materials [44,45]. Therefore, the observed crack initiation sites were described by a parameter of effective defect size √ area eff that was proposed by Murakami et al. [46], which has been experimentally verified for the Ti-6Al-4V alloy produced by conventional techniques [47,48] as well as by additive manufacturing [44,45]. The √ area eff parameter represents an area of a defect and a ligament between the defect and the free surface (described in more detail in [44,45]), as shown schematically in Figure 5b-f. The effective size of the defects in the PBF-LB Ti Grade 2 ranged from around 40 to over 150 µm (Figure 5b-f). As we marked the √ area eff parameter on the S-N curves in Figure 4a, we can clearly observe that the high-cycle fatigue life was reduced as the size of manufacturing defects increased. Masuo et al. [45] have recently shown that fatigue strength is inversely proportional to ( √ area eff ) 1/6 . In order to evaluate the influence of defect size on the fatigue strength, the high-cycle fatigue data for PBF-LB Ti Grade 2 was normalized in accordance with the ( √ area eff ) 1/6 parameter, as presented in Figure 4b. It is clear that after taking into account the defect size, scattering of the high-cycle fatigue results for PBF-LB Ti Grade 2 was much lower. detail in [44,45]), as shown schematically in Figure 5b-f. The effective size of the defects in the PBF-LB Ti Grade 2 ranged from around 40 to over 150 µm (Figure 5b-f). As we marked the √areaeff parameter on the S-N curves in Figure 4a, we can clearly observe that the high-cycle fatigue life was reduced as the size of manufacturing defects increased. Masuo et al. [45] have recently shown that fatigue strength is inversely proportional to (√areaeff) 1/6 . In order to evaluate the influence of defect size on the fatigue strength, the high-cycle fatigue data for PBF-LB Ti Grade 2 was normalized in accordance with the (√areaeff) 1/6 parameter, as presented in Figure 4b. It is clear that after taking into account the defect size, scattering of the high-cycle fatigue results for PBF-LB Ti Grade 2 was much lower.

Fatigue Crack Growth Rate of PBF-LB and UFG Ti Grade 2
The total fatigue lifetime is dependent on the crack initiation and the crack propa tion times [43]. As mentioned above, the fatigue crack initiation was strongly affected the size of the manufacturing defects in the PBF-LB Ti Grade 2 ( Figure 4). In this par comparison of the crack growth behavior in PBF-LB and UFG Ti Grade 2 is presented order to evaluate the fatigue crack growth rate, striation spacing analysis was conduct In the second stage of fatigue crack growth, it is assumed that each stress cycle produ one striation that corresponds to a crack growth rate at a given stress intensity fac range, ΔK [24,43]. As shown by Guo et al. [49], ΔK for an elliptical surface crack in a rou bar can be expressed as:

Fatigue Crack Growth Rate of PBF-LB and UFG Ti Grade 2
The total fatigue lifetime is dependent on the crack initiation and the crack propagation times [43]. As mentioned above, the fatigue crack initiation was strongly affected by the size of the manufacturing defects in the PBF-LB Ti Grade 2 ( Figure 4). In this part, a comparison of the crack growth behavior in PBF-LB and UFG Ti Grade 2 is presented. In order to evaluate the fatigue crack growth rate, striation spacing analysis was conducted. In the second stage of fatigue crack growth, it is assumed that each stress cycle produces one striation that corresponds to a crack growth rate at a given stress intensity factor range, ∆K [24,43]. As shown by Guo et al. [49], ∆K for an elliptical surface crack in a round bar can be expressed as: where ∆σ is the applied stress range on the minimum cross-section of the bar without a crack Φ = 1 + 1.464(a/c) 1.65 , a is the crack length, and c is the crack width. The factor Y(α,β,γ) is dependent on the specimen and crack geometry in the following way [49]: where α, β, γ are the following aspect ratios: α = a/d; β = a/c; γ = s/S (dimensions a, c, d, s, and S are presented schematically in Figure 6).  Figure 6 presents the results of striation spacing analysis for PBF-LB and UFG Ti Grade 2. The crack growth rate (represented by the striation spacing) is plotted as a function of the calculated stress intensity factor range ΔK. It is clear that fatigue striation spacing continuously grows with the higher applied ΔK, as shown in the exemplary SEM images for ΔK = 10.3, 13.2, and 14.6 MPa m 1/2 . In such a stage of stable crack growth, the fatigue crack propagation rate (da/dN) can be expressed by the Paris law: where C and m are material constants. The estimated values of Paris law constants were very close to each other, i.e., C = 4.0 × 10 −10 m/cycle and m = 2.7 for PBF-LB and C = 2.5 × 10 −10 m/cycle and m = 2.8 for UFG Ti Grade 2, which indicated their similar fatigue crack growth resistance. Typically, the Paris law exponent m for the conventionally manufactured Ti Grade 2 is in the range of 3.7-4.3, while the C constant reaches value of 1.8-7.9 × 10 −12 m/cycle (as shown in Table 2). The lower m and higher C value for PBF-LB and UFG Ti Grade 2 was indicated on the faster crack propagation. It has been already proved in many of the reports in the literature that a ultrafine-and nanograined microstructure enhances the fatigue crack growth rate [24,50,51]. The nanocrystalline or UFG metallic materials show a lower ability to strain hardening compared to their microcrystalline counterparts, which results in the lower energy dissipated at the crack tip during plastic deformation. The fatigue crack also propagates much easier in the nanocrystalline or UFG materials, and its  Figure 6 presents the results of striation spacing analysis for PBF-LB and UFG Ti Grade 2. The crack growth rate (represented by the striation spacing) is plotted as a function of the calculated stress intensity factor range ∆K. It is clear that fatigue striation spacing continuously grows with the higher applied ∆K, as shown in the exemplary SEM images for ∆K = 10.3, 13.2, and 14.6 MPa m 1/2 . In such a stage of stable crack growth, the fatigue crack propagation rate (da/dN) can be expressed by the Paris law: where C and m are material constants. The estimated values of Paris law constants were very close to each other, i.e., C = 4.0 × 10 −10 m/cycle and m = 2.7 for PBF-LB and C = 2.5 × 10 −10 m/cycle and m = 2.8 for UFG Ti Grade 2, which indicated their similar fatigue crack growth resistance. Typically, the Paris law exponent m for the conventionally manufactured Ti Grade 2 is in the range of 3.7-4.3, while the C constant reaches value of 1.8-7.9 × 10 −12 m/cycle (as shown in Table 2). The lower m and higher C value for PBF-LB and UFG Ti Grade 2 was indicated on the faster crack propagation. It has been already proved in many of the reports in the literature that a ultrafine-and nanograined microstructure enhances the fatigue crack growth rate [24,50,51]. The nanocrystalline or UFG metallic materials show a lower ability to strain hardening compared to their microcrystalline counterparts, which results in the lower energy dissipated at the crack tip during plastic deformation. The fatigue crack also propagates much easier in the nanocrystalline or UFG materials, and its deflection occurs less frequently than in their microcrystalline counterparts [24,51]. Cavaliere et al. [50] showed for Ti Grade 2 that the grain size refinement leads to the diminishment of fatigue crack growth resistance, and they reported, for Ti Grade 2 after equal channel angular pressing (ECAP), the Paris law constants of C = 1.8 × 10 −10 m/cycle and m = 2.4, which are very close to those observed in the current study for UFG Ti Grade 2. In turn, the Paris law constants of additively manufactured Ti Grade 2 are usually at a comparable level to their conventional counterparts ( Table 2), but their threshold stress intensity factor ∆K th is much lower (i.e., the fatigue crack starts to propagate earlier) [15,40]. Hasib et al. [40] reported C = 3.0-6.3 × 10 −12 m/cycle and m = 3.8-4.2 for vertically and horizontally laser-fabricated Ti Grade 2, which suggests its higher crack growth resistance in comparison to the current work. However, Rans et al. [14] and Xu et al. [52] showed for the laser-fabricated Ti-6Al-4V alloys that specimens built at an angle of 30-60 • to the building platform are mostly characterized by an enhanced fatigue crack growth rate (Table 2). Thus, the lower resistance to crack propagation of PBF-LB Ti Grade 2 investigated in this work is probably related to the applied building strategy (i.e., 30 • building orientation).

Effect of Manufacturing Defects on High-Cycle Fatigue of PBF-LB and UFG Ti Grade 2
The fatigue striation spacing analysis showed that the crack growth rate of PBF-LB Ti Grade 2 was close to that obtained for UFG Ti Grade 2 ( Figure 6), while its endurance fatigue limit was significantly lower (330 and 420 MPa for PBF-LB and UFG Ti Grade 2, respectively). This may somehow be linked with their different microstructures, i.e., acicular α' martensite in the PBF-LB Ti Grade 2, and ultrafine, equiaxed α phase grains in the UFG Ti Grade 2. As reported by Tao et al. [53], acicular α' microstructure may promote microstructurally small crack growth compared to the more homogeneous α + β lamellar microstructures, which is related to the easier crack initiation at sharp needles of the martensitic phase. Xu et al. [54] also proved for AM Ti-6Al-4V alloy that lamellar α + β specimens demonstrate higher fatigue strength than the α' martensite specimens. Similar findings were also reported by Hasib et al. [40] for the additively manufactured CP Ti Grade 2: they found that the transformation of α' to α phase grains and increasing the α phase grains both improved the fatigue crack growth resistance in the small crack regime. At higher crack lengths, the fatigue crack growth rate became insensitive to microstructural changes, as shown in the current study as well as in Figure 6. Nevertheless, it is commonly accepted that the extensive presence of defects/voids play a greater role in the high cycle fatigue life of AM Ti-based alloys [11]. Therefore, the significantly lower endurance fatigue limit of PBF-LB Ti Grade 2 investigated in this study was mainly related to the presence of manufacturing defects (such as pores and lack-of-fusion zones) formed during PBF-LB process, which became crack initiation sites (as presented in Figure 5). Such a phenomenon is commonly observed in the additively manufactured materials, which weakens their fatigue performance. Figure 7 shows a comparison of fatigue strength of conventionally and additively manufactured Ti-based materials with respect to their tensile properties. All plotted data is summarized in Table 3. Most of the fatigue data comes from the fully-reversed fatigue tests (R = −1). For other load ratios, the fatigue strength was recalculated using a Walker factor ((1-R)/2) 0.28 [55]. Typically, the ratio of the endurance fatigue limit to YS value for fully dense Ti-based materials is higher than 0.5 [24], which is also shown in Figure 7a. UFG Ti Grade 2 fulfilled this tendency with a ratio of 0.54. Unfortunately, this ratio is significantly lower for the additively manufactured Ti-based components (from 0.10 to 0.37) and clearly depends on the surface quality. The lowest ratios are observed for the as-built Ti-based elements, while fine polishing can highly improve their fatigue performance (Figure 7a). PBF-LB Ti Grade 2 analyzed within this work showed a relatively high ratio of fatigue limit to YS value (0.45) compared to other additively manufactured materials. This resulted from a precise surface preparation, appropriate stress relieving, and an applied building strategy. Moreover, a relatively low porosity (0.21%) of PBF-LB Ti Grade 2 should be also pointed out. Figure 7b shows the effect of porosity on the ratio of the endurance fatigue limit to YS. It is clear that this ratio (i.e., high-cycle fatigue performance) of the additively manufactured Ti-based materials can be significantly improved by limiting the porosity and number of manufacturing defects. The current work also showed that the fatigue lifetime can be significantly prolonged by decreasing the size of manufacturing defects. It was noticed that fatigue cracks were initiated mainly at the lack-of-fusion zones, too, showing the √ area eff parameter ranging from about 80 to 350 µm ( Figure 5). When the √ area eff parameter increased, the fatigue lifetime was reduced to a greater extent (Figure 4a). All of the abovementioned findings clearly show the necessity of reducing both the amount and the size of manufacturing defects in order to improve the fatigue performance of the additively manufactured Ti-based alloys. shown in Figure 7a. UFG Ti Grade 2 fulfilled this tendency with a ratio of 0.54. Unfortunately, this ratio is significantly lower for the additively manufactured Ti-based components (from 0.10 to 0.37) and clearly depends on the surface quality. The lowest ratios are observed for the as-built Ti-based elements, while fine polishing can highly improve their fatigue performance (Figure 7a). PBF-LB Ti Grade 2 analyzed within this work showed a relatively high ratio of fatigue limit to YS value (0.45) compared to other additively manufactured materials. This resulted from a precise surface preparation, appropriate stress relieving, and an applied building strategy. Moreover, a relatively low porosity (0.21%) of PBF-LB Ti Grade 2 should be also pointed out. Figure 7b shows the effect of porosity on the ratio of the endurance fatigue limit to YS. It is clear that this ratio (i.e., high-cycle fatigue performance) of the additively manufactured Ti-based materials can be significantly improved by limiting the porosity and number of manufacturing defects. The current work also showed that the fatigue lifetime can be significantly prolonged by decreasing the size of manufacturing defects. It was noticed that fatigue cracks were initiated mainly at the lack-of-fusion zones, too, showing the √areaeff parameter ranging from about 80 to 350 µm ( Figure 5). When the √areaeff parameter increased, the fatigue lifetime was reduced to a greater extent (Figure 4a). All of the abovementioned findings clearly show the necessity of reducing both the amount and the size of manufacturing defects in order to improve the fatigue performance of the additively manufactured Ti-based alloys. Figure 7. (a) Relation between endurance fatigue limit and yield strength of conventionally and additively manufactured Ti-based materials, and (b) influence of porosity on fatigue limit to yield strength ratio for additively manufactured Ti-based materials (based on data summarized in Table  3).  (a) Relation between endurance fatigue limit and yield strength of conventionally and additively manufactured Ti-based materials, and (b) influence of porosity on fatigue limit to yield strength ratio for additively manufactured Ti-based materials (based on data summarized in Table 3).

Conclusions
The aim of this study was to show how strong the effect of manufacturing defects in the CP Ti Grade 2 produced by PBF-LB process will be on its high-cycle fatigue life. For this purpose, the high-cycle fatigue performance of PBF-LB Ti Grade 2 was compared to its UFG counterpart processed by hydrostatic extrusion. Both materials exhibited similar yield strength (740 and 783 MPa for PBF-LB and UFG Ti Grade 2, respectively), suggesting their comparable high-cycle fatigue strength. To reduce the influence of surface roughness and residual stresses, PBF-LB Ti Grade 2 specimens were stress-relieved as well as precisely machined and polished before the fatigue tests. The main conclusions were as follows: 1.
PBF-LB Ti Grade 2 consisted of typical columnar prior β grains with an acicular martensite α' microstructure, while UFG Ti Grade 2 was mainly composed of fine, equiaxed α phase grains/subgrains with a size of 50-150 nm. What is important here is that a residual porosity of 0.21% was observed in the PBF-LB Ti Grade 2 by X-ray computed tomography.

2.
Despite having a similar yield strength, a significantly higher endurance fatigue limit was noticed for UFG Ti Grade 2 (420 MPa) compared to PBF-LB Ti Grade 2 (330 MPa). This resulted from the presence of manufacturing defects, such as pores and a lack of fusion zones. Fatigue cracks were initiated mainly at the lack of fusion zones, with the effective defect size √ area eff ranging from about 80 to 350 µm. When the √ area eff parameter increased, the high-cycle fatigue lifetime was reduced to a greater extent.

3.
Fatigue striation analysis showed that the fatigue crack propagation rate was not affected by manufacturing technology. The estimated values of Paris law constants were as follows: C = 4.0 × 10 −10 m/cycle and m = 2.7 for PBF-LB and C = 2.5 × 10 −10 m/cycle and m = 2.8 for UFG Ti Grade 2, which indicated their similar fatigue crack growth resistance.