Influence of α‐Precipitate Orientation and Distribution on the Deformation Behavior of the Additively Manufactured Metastable β‐Titanium Alloy Ti‐5553 Assessed by Cyclic Nanoindentation

The metastable β‐titanium alloy Ti–5Al–5V–5Mo–3Cr (Ti‐5553) has recently found growing interest as medical implant material due to its advantageous mechanical properties when compared to the up‐to‐date standard alloys. Besides biocompatibility, implant materials need to exhibit sufficient fatigue resistance. Herein, cyclic nanoindentation is applied up to a maximum cycle number of 105 to elucidate the influence of the local phase distribution on the cyclic deformation behavior of Ti‐5553, made by laser powder bed fusion of metals (LPBF‐M), in the (α + β)‐solution annealed state. By combining the localized cyclic mechanical loading and high‐resolution transmission electron microscopy, the influence of the presence and orientation of αp‐precipitates within the β‐grains on the cyclic deformation behavior and mechanisms is unraveled. αp‐phase orientation and distribution significantly contribute to the effectiveness of the precipitates as barriers to dislocation motion. A high density and trapping of dislocations are observed at α/β interfaces. The occurrence and size of the pile‐up surrounding the indents are correlated with the cyclic deformation behavior, and, thus, with the presence of αp‐precipitates. The gained improved knowledge of the phase‐dependent deformation behavior helps to better understand the fatigue performance of this alloy also on the macroscale.


Introduction
Titanium (Ti) alloys are in common use for orthopedic implants because of their excellent combination of mechanical strength, corrosion resistance, and biocompatibility. [1,2]The metastable β-alloy Ti-5Al-5V-5Mo-3Cr (wt%, Ti-5553) has recently found growing interest for load-bearing implants.As compared to the up-to-date gold standard, the (α þ β)alloy TiAl6V4, Ti-5553, exhibits a better combination of ductility, toughness, and Young's modulus. [3]ue to daily activities, load-bearing implants and, specifically, joint replacements have to sustain very high loads over millions of cycles. [4]Besides biocompatibility, implant materials hence need to exhibit sufficient fatigue resistance.It is, therefore, of prime importance to understand their cyclic deformation and fatigue behavior.Previous studies have reported on the influence of processing variables and follow-up treatments on the microstructure and fatigue behavior of additively [5] and conventionally [6][7][8][9][10][11][12][13][14] manufactured Ti-5553.Only a few of these have also investigated the cyclic deformation mechanisms. [12,14]esults are ambiguous, due to different loading conditions and different microstructures of the tested materials.For example, during pure compression fatigue loading, Ti-5553 with a β-annealed microstructure exhibited initial cyclic softening due to dislocation annihilation, which reduces constraints on dislocation mobility, and evolution of twin structures, such as detwinning and twin boundary degradation.With further loading, the material entered a saturation state, attributed to the flip-flop movement of dislocation dipoles. [13]Under fully reversed tension-compression loading, Ti-5553 with an (α þ β)microstructure showed plastic strain incompatibility between the α and β phases.In strain-controlled loading, the cyclic deformation behavior further depends on the strain amplitude.At low levels, some studies observed moderate hardening at the beginning of loading followed by a saturation stage, [12] while others reported only softening. [14]At intermediate amplitudes, moderate hardening preceded softening, [12] and at high amplitudes, pronounced softening occurred. [12,14]Cyclic hardening was attributed to the activation and interactions of multiple slip systems in the primary α (α p ) phase and the impingement of dislocation movement by α p /β boundaries.Softening was explained to be the result of massive dislocation annihilation, mainly of pre-existing dislocations, and cross-slip of dislocations in the α p -precipitates and the β-matrix. [12,14]onventional fatigue testing of macrospecimens requires a lot of material and a high number of specimens.Cyclic nanoindentation offers a fast and relatively simple approach to overcome these limitations. [15]18] Recently, cyclic nanoindentation has been used to assess the local fatigue properties of metals.[25][26] For closed-cell aluminum foams, cyclically indented six times with increasing loads, uniaxial stress-strain plots were constructed from the penetration depths and forces of the single cycles, and properties of individual microstructural phases and their volume fractions were identified. [23]The progression of indentation depth with the number of cycles exhibited two distinct regions for solution-treated and aged AZ61 Mg alloy [24] and duplex stainless steel, cyclically nanoindented in load control up to 300 cycles. [25]A primary or transient stage where the indentation depth rate decreased with the number of cycles preceded a secondary "steady-state" region, suggesting a balance between cyclic hardening and softening.In displacement-controlled tests up to a maximum number of cycles of 100, TiAl6V4 with a duplex microstructure with more than 90% α-phase exhibited cyclic softening for both, primary and lamellar α-phase, indicated by a decrease in peak stress. [26]To the best of our knowledge, there are only two reports so far on cyclic nanoindentation fatigue of metals up to a much higher maximum cycle number of 10 5 . [27,28]The tests performed on cross sections of struts extracted from A356.0 aluminum alloy open-cell foam [27] and of Mg-SiC nanocomposites [28] showed significant influences of the phase composition in a micrometer-sized interaction volume below the indent on the cyclic deformation behavior.
As reviewed above, the considerable difference in the deformation capability of the different phases in the metastable β-Ti alloy Ti-5553 may induce very heterogeneous deformation under cyclic loading conditions on the macroscale.This leads to complex relationships between phase morphology and distribution and cyclic deformation behavior.To elucidate such influences, we performed cyclic nanoindentation tests on this alloy in the (α þ β)-solution-annealed state up to a maximum cycle number of 10 5 , yielding information on the cyclic deformation behavior in loading regimes that are relevant to many applications.By combining cyclic nanoindentation and highresolution electron microscopy, we unravel the influence of different α-phase orientations and distributions within the β-grains on the deformation mechanisms under cyclic loading.The gained improved knowledge of the phase-dependent deformation behavior will help us to better understand the fatigue performance of this alloy also on the macroscale, ultimately paving the way to predict the fatigue response in silico for specific microstructures.

Material
Specimens for nanofatigue tests were extracted from the gauge length of a standard cylindrical fatigue specimen, provided by the Chair of Machine Tools and Production Engineering of Technische Universität Berlin (Figure 1).The specimen was produced by laser powder bed fusion of metals (LPBF-M) with an SLM Solutions 250 H machine (MTT Technologies GmbH, Germany) with its longitudinal axis at a 90°angle to the building platform from Ti-5553 powder made by plasma atomization (grain size 15-45 μm; D 50 = 34 μm; AP&C Advanced Powders & Coatings, Quebec, Canada).Following LPBF-M, the specimen was heat treated to generate a binary (α þ β)-microstructure. [29]he chemical compositions of the powder, as given by the supplier, and of the specimen after LPBF-M and after heat treatment, obtained by energy-dispersive X-ray spectroscopy (EDAX PV9800, installed on a CamScan REM Serie 2, Obducat, Sweden) at an accelerating voltage of 20 keV are given in Table 1 together with the used LPBF-M parameter settings.

Preloading Microstructural Investigation
Longitudinal and cross sections (Figure 1) were ground on SiC abrasive paper down to 500 grit and polished with diamond suspension down to a grain size of 9 μm.Grain size and phase distribution were evaluated by light microscopy (DMR, Leica, Germany) after etching with Kroll's reagent. [30]The sections were then repolished for 10 min with active oxide polishing solution (OP-S, Struers, Denmark) buffered with hydrogen peroxide and ammonia to achieve a smooth surface fit for evaluation of grain orientation and phase distribution by electron backscatter diffraction (EBSD).The EBSD measurements were performed at the Central Electron Microscopy Unit (ZELMI) of Technische Universität Berlin in a field-emission scanning electron microscope (SEM) DSM 982 GEMINI (ZEISS, Oberkochen, Germany) operated at 15 kV with a step size of 100-400 nm.Image analysis to obtain phase maps and inverse pole figures (IPFs) was done with the software OIM Analysis 6.0 (EDAX/ AMETEK, Mahwah, USA).

Nanofatigue Experiments
Nanofatigue experiments were performed on a Hysitron Triboindenter TI950 (Bruker Corporation, Massachusetts, USA) using a Berkovich tip.The surface of a cross section through an LPBF-M specimen was prepared in the same way as described above for the metallographic sections used for the EBSD measurements.24 indents were placed in a square map, spaced equally at a distance of 30 μm to avoid mutual interactions.Four additional indent positions were selected by visual inspection of etched surfaces; the regions of interest were distinguished by local variations in α-phase occurence.The identified positions were then indented cyclically after repolishing to remove the roughness induced by etching.
For nanofatigue loading, each site was indented cyclically to a maximum cycle number of 10 5 at a frequency, f, of 201 Hz.The minimum force, P mín , was 258 μN and the maximum force, P max , was 2888 μN, corresponding to a force amplitude, P a , of 1315 μN and a mean force, P m , of 1573 μN (indents 1-24).The four positions placed in defined regions of interest (addressed in the following as indents A, B, C, D) were loaded with P mín = 456 μN and P max = 2946 μN (P a = 1245 μN, P m = 1701 μN).The minimum load ensured constant contact between the tip and the sample surface throughout the tests in all cases.
Because of limitations in the data acquisition rate and the amount of data that can be stored, the number of data points available was not high enough in the high-frequency loading cycles to evaluate the force/indentation depth curves.
Therefore, low-frequency, so-called "measurement cycles" at f = 0.05 Hz (Figure 2a) were inserted at regular intervals to yield force/indentation depth hysteresis loops with sufficient data points (Figure 2b).Further, for indents 1-24, static "holding" segments at 10% of the maximum load were introduced before and after the measurement cycles for thermal drift correction. [31]he force/indentation depth-hysteresis loops were evaluated according to protocols used in classical fatigue testing by customized code based on Python. [32]The cyclic deformation behavior was characterized by the development of the plastic indentation depth amplitude, D a,p , determined as the half width of the hysteresis loop at mean force.The development of the ratios of D min to D max over the cycle number, N, and the change of plastic deformation between cycles, ΔD min , induced by repeated application of the force amplitude over N, and represented by the change in minimum depth (D min ) between consecutive measurement cycles, was analyzed to evaluate the cyclic creep behavior.

Microstructural and Morphological Investigation of Fatigue-Induced Nanoindent Characteristics
The four nanoindents "A" to "D," placed in defined regions of interest, were imaged in a high-resolution SEM (HRSEM; Gemini SEM500 NanoVP, Zeiss, Oberkochen, Germany) in Table 1.LPBF-M parameter settings used to manufacture the standard cylindrical fatigue specimen, together with the chemical composition (wt%) of the Ti-5553 powder, as given by the supplier, and of the specimen after LPBF-M and heat treatment, obtained from energy-dispersive X-ray spectroscopy.the backscattered electron mode at a voltage of 8 kV at a working distance of 7.6 mm.Microstructure and dislocation structure and density in the volume directly beneath these indents were investigated by transmission electron microscopy (TEM), using a Tecnai G 2 20 S-TWIN (FEI Company, OR, USA) at an operating voltage of 200 kV in the bright-field mode.For TEM observation, thin foils were prepared using the focused ion beam (FIB) technique (FEI Helios NanoLab 600; Field Electron and Ion Company, Hillsboro, USA).One long edge of the foil was oriented parallel to the indentation direction, and the section was placed as precisely as possible through the tip of each nanoindent.To protect the foil against plastic deformation and the sample surface from the gallium ions, the sample was covered with a thin platinum layer before ion-beam milling.Although we cannot be sure that our TEM foils were placed right through the tip, we are sure that they passed very close to it, given that the maximum indentation depth after fatigue loading observed from the triangular profile in the TEM micrographs (compare Figure 11) matched the range of depths of the four indents "A" to "D" (182-261 nm).All SEM, FIB, and TEM work was performed at the Central Electron Microscopy Unit (ZELMI) of Technische Universität Berlin.
To allow qualitative and quantitative evaluation of indent and pile-up morphology and size, all cyclic nanoindents and the surrounding surfaces were imaged using the scanning probe microscopy (SPM) mode of the nanoindenter.Both topography and gradient images were evaluated qualitatively and quantitatively.The projected area (A p ), the outer pile-up area (A p-u ) and the pile-up volume (V p-u ) were determined after background subtraction using Fiji, [33,34] where the best fit for A p and A p-u was found by visual inspection of the SPM topography image, as shown for a typical example in Figure 3. V p-u was determined by the integration of all pixels under the pile-up area.Nanoindent and pile-up profiles were measured using Gwyddion, [35] from which the maximum pile-up height (h p-u,max ) was obtained, as exemplified in Figure S1, Supporting Information.

Microstructure
The material has a biphasic microstructure with small α p -precipitates highly dispersed within the grains and at the grain boundaries of the retained β-matrix (Figure 4, and 5e,f ).In lowmagnification light micrographs (Figure 4a-d), the grain boundaries appear as bright stripes, some of which contain black lines.Higher magnifications (Figure 4e,f ) reveal that these bright stripes consist of β-phase and that the black lines are α p -particles arranged like a rope of pearls approximately in the center of the β-stripe.
Digital image analysis of EBSD data gave phase fractions of about 88% and 12% for β and α p , respectively, for both transverse and longitudinal sections (Figure 5a,b).The β-grains have square cross sections orthogonal to the LPBF-M build direction, and a slightly elongated shape in the longitudinal orientation, parallel to the build direction.EBSD IPF (Figure 5c,d) show no crystallographic texture.
By light microscopy, lighter and darker regions are visible in both cross and longitudinal sections.Each of these regions comprises several grains (Figure 4a,b).EBSD-IPF views (Figure 5e) and higher-magnified SEM micrographs (Figure 5f ) reveal that the differences in gray value are due to different densities, shapes, and amounts of sections of α p -precipitates in the field of view, as shown exemplarily in Figure 6.The different views reveal that the precipitates are acicular, with their diameters varying along their length.Hence, the differences in the appearance of α p come from their different orientation and, thus, the appearance of the exposed sectioned plane.Even though the surface comprises regions where the α p -precipitates exhibit a preferential orientation, EBSD measurements revealed no overall preferred crystal orientation and no orientation relationship between the α-phase and the surrounding β-matrix.

Cyclic Deformation and Creep Behavior
The cyclic deformation behavior is displayed in Figure 7 by plots of the plastic displacement amplitude D a,p versus N. On a macroscopic view, we observe stages of hardening, saturation, and softening.However, within each of these three stages, fluctuations of D a,p occur.The indents differ by the extent of the stages relative to each other and by the size of the fluctuations.The first stage comprises the first ten cycles.Here, most nanoindents present overall hardening, visible by a net decrease in D a,p .This stage is characterized by moderate alterations between hardening and softening for more than 50% of these indents, by soft alterations for a quarter of the indents and by strong alterations for about a fifth.Indents 3 and 16 (Figure 7b) are examples of moderate and soft alterations, respectively.Only about 3% of the nanoindents, for instance indent 1 (Figure 7b), exhibit softening following pronounced hardening in the first cycle and subsequent strong fluctuations.For most nanoindents, the initial hardening or softening is followed by weak further softening for loading up to 10 4 cycles: more than half of the indents (54%) show an increase in D a,p with pronounced fluctuations, 18% with small fluctuations and 7% without fluctuations (compare indents 1 and 16 in Figure 7b).Only about one-fifth of the nanoindents, for example, indent 3 (Figure 7b), exhibit a low amount of further hardening: 18% show a decrease in D a,p with fluctuations, and 3% without fluctuations.During further loading to the maximum number of cycles of 10 5 , the curves of most indents (75%) decrease with fluctuations, 22% increase with fluctuations, and 3% of them present a pronounced increase with fluctuations.
The progressions of the ratios of D min to D max and of ΔD min over the number of cycles were analyzed to further evaluate the amount of plastic deformation per cycle and the cyclic creep behavior, respectively.The curves for D min /D max over N (Figure 8) progress in similar ways, with an overall increase in D min /D max , but they differ in the extent of the increase: some curves progress to higher and others to lower values.
ΔD min represents the incremental, nonreversible deformation, induced by repeated loading, over the entire loading history.As the number of cycles between the "measurement cycles" is not constant, and because small differences in the minimum load are not avoidable, ΔD min was normalized by the number of cycles over which the change occurred and by the minimum load, which gives us ΔD min-norm (Figure 9).An overall decrease in ΔD min-norm over N is seen for all indents (Figure 9a-c), however, with high fluctuations from cycle to cycle at the beginning of loading, up to N = 10.Some indents even present negative ΔD min-norm values.Up to the 100th cycle, ΔD min-norm approaches values between 10 À4 and 3 Â 10 À4 nm μN À1 .Over the further course of loading (10 4 ≤ N ≤ 10 5 ), an overall decrease in ΔD min-norm with slight alterations below 2 Â 10 À6 nm μN À1 is observed.Note, however, that the ΔD min-norm values are averaged over increasing numbers of cycles with increasing N, which is expected to add to a smoother progression.The three typical progressions (Figure 9d) highlight the pronounced differences in the extent of the fluctuations seen over the first ten cycles.Further, for each of the indents, ΔD min-norm approaches clearly distinguishable levels over the further course of loading (Figure 9e,f ).

Cyclic Nanoindent Morphology
Nanoindent and pile-up size and morphology were evaluated quantitatively based on the SPM images.Maximum indentation depth after fatigue loading (D max at the maximum number of cycles, N = 10 5 ), projected indent area (A p ), pile-up area (A p-u ), pile-up volume (V p-u ), and maximum pile-up height (h p-u,max ) are shown for all nanoindents in Table 2.The linear correlation    coefficients (R) for the different parameters are summarized in Table 3.The strongest correlations are seen between D max (N = 10 5 ) and A p (R = 0.78), and between A p and A p-u (R = 0.71), whereas the weakest correlations were found for A p-u and h p-u,max (R = 0.11) and for h p-u,max and V p-u (R = 0.29).
Figure 10 displays SPM topography images and 3D surface plots of typical nanoindents with different cyclic deformation behavior, as described in Section 3.2.Indent 1 (Figure 10a) is located in a surface region comprising α p -precipitates oriented parallel to each other.It exhibits the largest indent and pile-up sizes, regarding area (A p , A p-u ) and maximum height (h p-u,max ), but an intermediate pile-up volume (V p-u ).In the surface region surrounding indent 3, the α p -precipitates are transversely located (Figure 10b).This indent is about 21% smaller than indent 1 (A p ).Its lower deformation compared to indent 1 is also represented by smaller values of A p-u and h p-u,max .However, indent 3 has the highest V p-u .Indent 16 (Figure 10c) is even smaller (A p ) with very little pile-up, as measured by V p-u , although the surface microstructure surrounding indent 16 is very similar to that of indent 1.
Indents "A" to "D" were placed in selected areas of the specimen surface at positions with differences in the local distribution and surface appearance of the α-phase (see HR-SEM insets in Figure 11).Indent A is located in a surface region consisting of β-phase only.It has a large size and pile-up, mainly on its left edge.Indents B to D were placed in regions with α p -precipitates visible on the surface.While indent B was made in a region containing precipitates with a preferred orientation, indents C and D sit in surface regions with a relatively high content of α p -precipitates, oriented at different angles to each other.Both indents C and D hit α p -precipitates, while indent B sits in between the precipitates.Intermediate nanoindent and pile-up sizes are observed for indent B, and both values are smaller than for indent A. For indent C, the precipitates appear to be agglomerated, with a small or no distance between them.This nanoindent has an indent area similar to indent A, however, with a smaller pile-up area.Indent D exhibits the smallest indent area among the four indents, without significant pile-up.

TEM Investigation
TEM (Figure 11) was used to evaluate the microstructure and the dislocation density in volumes below the indents "A" to "D". Figure 11a shows nearly pure β-phase in the volume beneath indent A, with only one α p -precipitate visible in the plane of the TEM foil.A high dislocation density is observed along the grain boundaries.Further, twins are seen near the indent impression.For indent B (Figure 11b), a region with a high content of α p -precipitates is observed, and a high dislocation density is seen mainly along grain or phase boundaries.A high number of α p precipitates with different orientations is also revealed in the volume directly beneath indent C (Figure 11c).In this case, a higher dislocation density appears to be trapped between adjacent, transversely positioned α-precipitates.In the volume beneath indent D (Figure 11d), three α p -precipitates are oriented parallel to each other, at an acute angle of about 135°to the Table 2. Results of the quantitative analysis of indent and pile-up size: projected indent area (A p ), pile-up area (A p-u ), pile-up volume (V p-u ), and maximum pile-up height (h p-u,max ), together with the maximum indentation depth after fatigue loading (D max (N = 10 5 )) (n = indent number).The smallest and greatest values for each parameter are underlined and printed in bold, respectively.surface.Around these particles, a high dislocation density is observed.

Discussion
We used cyclic nanoindentation to characterize the influence of the local microstructure on the cyclic deformation behavior of Ti-5553 made by LPBF-M.Our results show a strong correlation between the cyclic deformation data, the microstructure in the volume beneath the nanoindents, and the fatigue-induced surface morphology and dislocation structure.The orientation and distribution of α p play a critical role in the cyclic deformation mechanism of this metastable β-Ti alloy, as discussed in detail in the following sections.

Microstructure
Through heat treatment of the as-printed specimens below the β-transus temperature, we achieved an (α þ β)-microstructure, with small α p -particles evenly distributed in the β-matrix, as to be expected based on results reported for classically manufactured Ti-5553. [36,37]The α p -phase fraction in our material is in the lower range of values reached for the nonadditivelymanufactured materials (12% vs. 10% [38] to 26% [39] ).Further, in contrast to α p -chevrons, [40] we observe singular, acicular particles, which may be due to the fundamentally different processing conditions before the heat treatment.Over significant regions of each β-grain, the α p acicular precipitates are co-aligned with their long axes parallel to each other; however, an overall preferred orientation is neither observed within a single grain nor between grains.Further, our EBSD measurements do not indicate an overall preferred crystal orientation and they do not hint at an orientation relationship between the α p -phase and the surrounding β-matrix.The latter result differs from the observation of others who reported that the α pphase has a Burgers orientation relationship with the β-matrix in (α þ β)-solution annealed Ti-5553. [41]A likely explanation is differences in the processing of conventional and additively manufactured Ti-5553.The conventional process involves thermomechanical treatments before the actual heat treatment.Thus, a lamellar (α þ β) microstructure is the starting point, while in our case it is pure β, which has neither been plastically deformed nor recrystallized.

Cyclic Deformation and Creep Behavior
We observe typical changes in hysteresis parameters (D ap , D min /D max , and ΔD min-norm ) over the number of cycles.The overall trend of the plastic displacement amplitude (Figure 7) over the whole test reveals three subsequent stages of hardening, saturation, and softening.Reports on the behavior of conventionally processed Ti-5553 on the macroscale differ from our observation, and they are not consistent: only cyclic softening, cyclic softening followed by saturation, or cyclic hardening followed by softening were observed. [12,42,43]Microstructural and compositional differences are one likely reason for the differences.All the reports refer to conventionally processed metastable β-alloys, with different compositions and heat treatments, compared to each other and our alloy.Moreover, classical macrofatigue tests reveal an average response over the microstructural constituents, whereas we probe the local interactions of phases with the deformation mechanisms (dislocation formation and movement, twinning), without averaging.Thus, we extract the influence of local structural inhomogeneities on the cyclic deformation behavior, which also explains the scatter between different indents (= regions) and the fluctuations we see in the progression of some hysteresis parameters (see below).
The second parameter that we evaluated, ΔD min-norm , decreases continuously and significantly with increasing numbers of cycles, while D min /D max increases steadily.Like D ap , ΔD min-norm exhibits significant fluctuations at the beginning of the tests.Such fluctuations are not seen for D min /D max .All curve progressions indicate a decrease in plastic deformability over the course of loading.The ratio of the minimum displacement reached in one cycle after unloading from the maximum load (which resulted in D max ), D min /D max , further hints at an overall more elastic unloading behavior with ongoing cyclic deformation, which correlates with the saturation observed in the progression of D a,p .
Our TEM investigations suggest that the interaction of dislocations with α p -precipitates is the most important cyclic deformation mechanism influencing cyclic hardening and softening and cyclic creep.The existence and orientation of the α p -precipitates below and around the indents influence the formation of dislocation structures.Most nanoindents exhibit alternating hardening and softening with an overall trend for smaller plastic displacement amplitudes (cyclic hardening) over the first ten cycles.Based on observations from macrofatigue tests, [12,14] we hypothesize that the repeated indentation activates multiple slip systems, as well as interactions of dislocations with each other and with nearby α p -precipitates, leading to hardening.As for macrospecimens, softening may arise from dislocation annihilation due to mutual dislocation impingement.Such dislocation annihilation has been stated to be the main reason for the predominance of cyclic softening in (α þ β)-Ti-5553 and (α þ β)-Ti-1023. [12,14,42]Most likely, these processes occur simultaneously under the localized relatively high loads and the multiaxial stress and strain state in the confined interaction volume below and around the indent.In the further course of loading, for 10 ≤ N ≤ 10 4 , we observe only small further changes in the plastic deformation amplitude, with some indents showing overall hardening, and others overall softening.In this "nearly saturation" state, therefore, either the described hardening or the softening mechanisms are dominant.Further, with ongoing loading, more dislocations can be activated and interact with differently oriented α p -precipitates in the indented volume, and the interaction volume expands, to a smaller or greater extent, depending on the existence and orientation of α p -particles nearby.Transversely placed α p -precipitates block the motion of the dislocations more effectively than α p whose long axis is oriented orthogonal to the surface, that is, parallel to the indentation direction (compare Figure 11c,d).Thus, the interaction volume can expand more in the latter case, overcoming possible dislocation annihilation and strengthening the β-matrix.α p orientation has also been reported to be an important factor influencing the cyclic deformation response of conventionally manufactured Ti-5553 on the macroscale, by influencing the prevalent micromechanisms. [12]Here, α p -precipitates in one sample deformed to different strain levels depending on their orientation to the loading direction.
For N ≥ 10 4 , most nanoindents exhibit hardening, and only a few show softening.Hardening may be explained by gradual activation and increasing interactions of multiple slip systems in the α p -precipitates, together with the impingement of α/β phase boundaries to dislocation movement. [12]Softening is likely due to new dislocation arrangements occurring in α p and in the volume below the indents, thereby facilitating plastic deformation. [12,14]Additionally, cyclic softening can be intensified with dislocations relocating from regions of high dislocation density to regions of low density. [44]nother mechanism is twin formation, shown by β-twins initiated at grain boundaries during cyclic nanoindentation (see red arrow in Figure 11a).With increasing deformation, twin boundaries can progressively form and effectively block dislocation movement.
Especially during the first ten cycles, we observe relatively large fluctuations in the progressions of D ap and ΔD min-norm over N.Such fluctuations are also seen in the further course of loading for many of the indents, however with considerably smaller amplitudes.It is especially noteworthy, that ΔD min-norm occasionally even acquires negative values.These indicate that the indenter is pushed up, instead of being pushed to the same or a bigger depth than in the cycle before.A similar behavior was observed during cyclic nanoindentation of an Al-Si alloy. [27]It may be explained by the release of residual stresses due to the cyclic plastic deformation.Residual stresses may result from thermally induced imbalances during LPBF-M, where fast heating and cooling in nearby regions may lead to quickly changing states of thermal expansion and contraction. [45,46]An additional cause can be modifications of the local microstructure due to the β !α phase transformation during the heat treatment. [47]All these processes can lead to complex residual stress/strain states.Further, the LPBF-M process and the subsequent heat treatment promote the formation of high dislocation densities primarily in the β-grain boundaries and in the α p -precipitates (Figure S2, Supporting Information).Under repeated loading and unloading cycles, these dislocations can be released and interact with each other and other dislocations.If this occurs stepwise, to different amounts in different cycles, fluctuations, that is hardening and softening, alternating from cycle to cycle or over tens to hundreds of cycles, are seen.

Fatigue-Induced Indent Characteristics
The quantitative observations of indent and pile-up size and morphology correlate well with the development of the cyclic deformation and creep response.Larger projected areas (A p ) correlate with greater indent depths (D max ), suggesting an overall lower resistance to cyclic plastic deformation in the indented volume.This is reflected by higher values of D min /D max and ΔD min-norm curves and pronounced cyclic softening for N ≥ 10 4 (see, e.g., nanoindent 1).Correspondingly, the smallest A p and D max values correlate with cyclic hardening and the lowest values for ΔD min-norm (see, e.g., nanoindent 16).
The extent of pile-up is strongly influenced by the microstructure surrounding and below the indents, determining to what extent plastic deformation is hindered in the volume below the indent.For our material, the values thus depend on how the precipitates influence the dislocation motion.For example, a high content of precipitates with differing orientations will effectively restrict the movement of the dislocations deeper into the material (see, e.g., Figure 11c).Consequently, they cause a decrease in the amount of plastic deformation. [48]Hence, a strong pile-up along the flanks of the indent appears as excessive material pushed out at the surface, as also reported for an Al-Si alloy. [27]However, indents in pure β-regions present large pile-up sizes (e.g., nanoindent A) as well.In this case, dislocations are more confined to the surface due to the progressive formation of twins in β-grains (Figure 11a) and large pile-up happens above the twin boundaries.
Cyclic indentations performed in regions with a relatively high content of widely spaced α p -precipitates have intermediate sizes and large pile-up volumes (e.g., nanoindent B, Figure 11b).Here, precipitates may be located near/on the surface, in the volume sideways of the indent or in the volume below the indent.Such precipitates favor the formation of dislocation structures because the growth of α p during the heat treatment deforms the β-matrix, causing considerable stress and thus generating dislocations.During cyclic indentation, the high dislocation density is released from the α p -precipitates that were directly encountered by the indenter.These dislocations interact with each other and with the precipitates, offering resistance to dislocation motion.However, a preferable placement of the precipitates still gives some space for dislocation movement into deeper areas in the volume.This leads to an intermediate cyclic plastic deformation state, as exemplified by indent 3 in Figure 9f.
In comparison, small nanoindents usually arise from cyclic indentation performed directly on α p -precipitates, which offer a relatively high resistance to deformation.When encountering one or more precipitates, the indenter cannot penetrate further into the material.An underlying microstructure with fewer and more preferably oriented α p enables dislocation movement without significant restrictions, as exemplified in Figure 11d.A large volume of material is plastically deformed and the dislocations move deeper below the indent, if only a low amount or no α p is present.In this case, much less material is pushed out at the edges of the indent, resulting in a very small pile-up size.

Summarizing Model Mechanism
Summarizing our results, we propose the interaction mechanism shown schematically in Figure 12.Precipitates with a preferred orientation where their long axes are parallel to the indentation direction are less effective hindering dislocation slip (Figure 12a) than precipitates that are not coaligned (Figure 12b).The latter arrangement effectively hinders the expansion of the interaction volume, thus fostering hardening due to the fast development of a high dislocation density in a confined volume.Accordingly, a high number of precipitates is more effective than a lower number, hindering dislocation movement faster, and a low or no content of α p results in more space for the dislocation mobility and thus higher plastic deformation values and more cyclic creep (Figure 12c).

Conclusion
We used cyclic nanoindentation to investigate local fatigue processes in an LPBF-M β-metastable Ti-5553 alloy with a binary (α þ β) microstructure.The α p -precipitates play an important role in the local fatigue behavior.1) Dislocation-based deformation mechanisms are the main origin of cyclic softening, cyclic hardening, and creep processes during cyclic nanoindentation.2) A strong correlation between the microstructure in the volume beneath the nanoindents and the dislocation reaction was observed: α p -phase orientation and distribution within the β-grains significantly contribute to the effectiveness of the precipitates as barriers to dislocation motion.High density, gathering, and trapping of dislocations were observed at α/β interfaces.
3) Pile-up occurrence and size are determined by the local plastic deformability, which in turn is significantly influenced by the presence and orientation of α p -precipitates. 4) Our findings differ from the results reported for the macrofatigue behavior of (α þ β)-Ti-5553 alloy, as our testing approach considers the influence of local structural inhomogeneities on the cyclic deformation.
Concluding, our results highlight the high potential of cyclic nanoindentation to elucidate the influence of the local microstructure on the cyclic deformation mechanisms of two-phase alloys, such as the novel implant alloy investigated.The gained understanding of the local interactions is the basis for improving the fatigue performance of this alloy on the macrolevel.

Figure 1 .
Figure 1.Specimens used for microstructural investigations and nanofatigue tests, prepared from the gauge length of a standard cylindrical fatigue specimen produced by LPBF-M.

Figure 2 .
Figure 2. a) Load function used for the nanofatigue tests consisting of alternating blocks of high-frequency loading at f = 201 Hz (marked in red, "loading cycles") and of low-frequency loading at f = 0.05 Hz (marked in black, "measurement cycles").Note that the force amplitude and the mean force were the same for both blocks; for clarity, the loading cycles are only depicted as red lines at mean force, with an indication of the loading times.b) Schematic representation of a typical force/indentation depth hysteresis loop from which the maximum depth (D max ), the minimum depth (D min ), and the plastic indentation depth amplitude (D a,p ) are determined.

Figure 3 .
Figure 3. Morphological evaluation of cyclic nanoindents: a) SPM topography image of a typical example, with the αand β-phase appearing in dark and bright gray, respectively; b) typical selection of the projected indent area; c) pile-up area, determined by visual inspection.

Figure 4 .
Figure 4. a-f ) Light micrographs of polished and etched cross (a,c,e) and longitudinal (b,d,f ) sections reveal a biphasic microstructure of α p (dark gray)finely distributed in retained β-matrix (bright gray).Two regions with different gray values are observed: a lighter one in which the α-precipitates seem to be more elongated and mostly oriented in a preferential direction (a-d), and a darker one in which the α-precipitates seem smaller with random orientation (e,f ).At smaller magnification (a,b), the grain boundaries appear as bright stripes, as if consisting only of β-matrix.Higher magnifications reveal darker areas within these stripes, which are α-precipitates arranged like a rope of pearls.

Figure 5 .
Figure 5. a,b) EBSD phase distribution measurements on transverse (a) and longitudinal (b) sections confirming the existence of a biphasic microstructure with a phase fraction of about 88% β-phase and 12% α-phase.c,d) EBSD-IPF results of cross (c) and longitudinal (d) sections showing the structure of the shape and orientation of the β-grains.The grains are elongated in the LPBF-M build direction with a clearly preferred orientation, yet without crystallographic texture.e,f ) Higher magnified EBSD-IPF (e) and SEM (f ) images showing the α-precipitates differing in orientation and sectioning to the surface.

Figure 6 .
Figure 6.Schematic representation of the crystallographic orientation of α p based on the EBSD-IPF maps: differences in the appearance of α p come from their different orientations and therefore different sectioning to the surface.

Figure 7 .
Figure 7. Cyclic deformation curves, D a,p over N, for a) all indents and b) typical examples, representing the different progression types (nanoindents 1, 3, and 16).

Figure 8 .
Figure 8. a) D min /D max over N for all indents.b) Examples of indents that differ in their extent of curve progression.

Figure 10 .
Figure 10.3D surface plots and SPM topography images (insets in the upper-right corners) of cyclic nanoindents with different, typical morphologies: a) indent 1, with a large projected area, large pile-up height, and high indentation depth; b) indent 3, with intermediate projected area, pile-up height, and indentation depth values; c) indent 16, with a small pile-up height, projected area, and indentation depth.Note that for better visibility of the nanoindent in the 3D surface plots, a different scale of the z-axis (depth of the indent) as compared to the lateral scale was chosen.

Figure 11 .
Figure11.a-d) Bright-field TEM micrographs of the volumes beneath the indents "A" to "D" together with HRSEM images of the tested surface (insets, lower left corner).(a) Indent A was made in a surface region without α-precipitates, and only one α-precipitate is visible below the indent in the plane of the TEM foil; high dislocation densities exist along the grain boundaries, and twinning (red arrow) is also observed.(b) Indent B sits in a region with a high content of α-precipitates, both on the surface and in the volume surrounding the indent in the plane of the TEM foil.Regions of high dislocation density are seen, mainly along grain or phase boundaries.(c) Indent C was also placed in a surface and volume region with a high content of α-precipitates.They, however, exhibit different orientations, and the distances between the α-particles are smaller than for indent B. A high dislocation density is observed between two adjacent precipitates, oriented nearly transversely to the indentation direction.(d) Indent D was performed in a region with a lower α-phase content than seen for indent "C".The precipitates are oriented parallel to each other, and one precipitate is included in the indented area (inset).Regions of higher dislocation density are observed surrounding the precipitates.

Figure 12 .
Figure 12.Schematic representation of dislocation distribution and structures in the volume beneath cyclic nanoindents: a) dislocation allocation affected by a low number of α p -precipitates oriented in a way such that a direct path for the dislocations toward deeper regions is available; b) high content of differently oriented α p , such that a high dislocation density develops and dislocations are trapped between the transversely positioned precipitates; c) indent surrounded only by the homogeneous β-matrix, yielding regions of high dislocation densities along the grain boundaries. 1 = indent; 2 = grain boundary; 3 = low dislocation density; 4 = high dislocation density; 5 = very low dislocation density.

Table 3 .
Linear correlation coefficients (R) between the indent and pile-up parameters given in Table2.The two weakest values of R are underlined, and the two strongest values are given in bold font.