Experimental Correlation of Mechanical Properties of the Ti-6Al-4V Alloy at Different Length Scales

metals

Article Experimental Correlation of Mechanical Properties of the Ti-6Al-4V Alloy at Different Length Scales

Víctor Tuninetti 1,* , Andrés Felipe Jaramillo 1 , Guiomar Riu 2, Carlos Rojas-Ulloa 1 , Amna Znaidi 3, Carlos Medina 4 , Antonio Manuel Mateo 2 and Joan Josep Roa 2,*

1 Department of Mechanical Engineering, Universidad de La Frontera, 4780000 Temuco, Chile; [email protected] (A.F.J.); [email protected] (C.R.-U.) 2 Department of Materials Science and Engineering (CIEFMA), Barcelona School of Engineering (EEBE), Universitat Politècnica de Catalunya-BarcelonaTech, 08019 Barcelona, Spain; [email protected] (G.R.); [email protected] (A.M.M.) 3 Laboratory of Applied Mechanics and Engineering LR-MAI, University Tunis El Manar–ENIT BP37, Tunis 1068, Tunisia; [email protected] 4 Department of Mechanical Engineering, Universidad de Concepción, 4030000 Concepción, Chile; [email protected] * Correspondence: [email protected] (V.T.); [email protected] (J.J.R.); Tel.: +56-452325984 (V.T.); +34-93-413-41-39 (J.J.R.)

Abstract: This article focuses on a systematic study of a Ti-6Al-4V alloy in order to extensively characterize the main mechanical properties at the macro-, micro- and submicrometric length scale under different stress fields. Hardness, elastic modulus, true stress–strain curves and strain-hardening exponent are correlated with the intrinsic properties of the α- and β-phases that constitute this alloy. A systematic characterization process followed, considering the anisotropic effect on both orthogonal crystallographic directions, as well as determining the intrinsic properties for the α-phase. An analytical relationship was established between the flow stress determined under different stress fields, testing geometries and length scales, highlighting that it is possible to estimate flow stress under Citation: Tuninetti, V.; Jaramillo, A.F.; compression and/or tensile loading from the composite hardness value obtained by instrumented Riu, G.; Rojas-Ulloa, C.; Znaidi, A.; nanoindentation testing. Medina, C.; Mateo, A.M.; Roa, J.J. Experimental Correlation of Keywords: titanium alloys; plastic anisotropy; tension–compression asymmetry; mechanical properties; Mechanical Properties of the Ti-6Al-4V nanohardness; Young’s modulus; tensile–compression tests Alloy at Different Length Scales. Metals 2021, 11, 104. https://doi.org/ 10.3390/met11010104 1. Introduction Received: 7 December 2020 Accepted: 3 January 2021 Titanium alloys are attractive engineering materials for the aerospace industry, mainly Published: 7 January 2021 because of their high speciﬁc strength and ductility at low and moderate temperatures [1–3]. In particular, Ti-6Al-4V is the most widely used titanium alloy due to a proper balance Publisher’s Note: MDPI stays neu- of processing characteristics such as good castability, plastic workability, heat treatability tral with regard to jurisdictional clai- and weldability [4]. In recent years, the deformation processes operating in α- and β-phase ms in published maps and institutio- titanium alloys have been extensively investigated by means of advanced characteriza- nal afﬁliations. tion techniques [5–7]. The predominant constituent phase of this Ti-alloy, low-symmetry hexagonal-structured α-phase, as well as α-/β-interfaces, exhibit remarkable elastic and plastic anisotropy [8,9]. The primary cause of the anisotropic behavior of polycrystalline alloys is the preferred orientation of grains, crystallographic textures, due to working pro- Copyright: © 2021 by the authors. Li- censee MDPI, Basel, Switzerland. cesses [10]. Therefore, properties of polycrystals can be computed as averages of weighted This article is an open access article values from the individual crystal orientations based on the texture [11]. distributed under the terms and con- The Ti-6Al-4V alloy is well known to exhibit anisotropic mechanical behavior through- ditions of the Creative Commons At- out the elastoplastic range, as reported in [2,8,12–14]. This anisotropic behavior is com- tribution (CC BY) license (https:// monly characterized by properties such as Young’s modulus, initial flow stress and strain- creativecommons.org/licenses/by/ hardening rate obtained from tensile and compression tests in different directions of the 4.0/). material [10,15–17]. In recent years, the nanoindentation technique has been presented as

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an alternative to the conventional testing methods because it is simple, fast, nondestructive, relatively inexpensive and requires a minimum amount of material [18–20]. In this context, the stress and strain states induced by instrumented nanoindentation are clearly different from the states in uniaxial testing. The deformation field induced by a sharp nanoindenter also varies according to the analyzed location. Biaxial stretched regions are localized in the surface surrounding the indentation imprint, and the region directly below the nanoindenter tip exhibits compressive triaxial deformations. It is worth noting that the stretched area appears because much of the portion of the material presents an elastic strain field, and the plastic region is localized very close to the indenter tip. The elastic zone acts as a rigid body imposing displacement constraints to the plastic zone, producing a triaxial or combined stress state. As is clearly evident in the literature, the investigation of mechanical behavior at the local length scale constitutes a fundamental and active research topic for Ti-6Al-4V alloys, as found in [21–23]. It is well established that the mechanical response at the micrometric and submicrometric length scales differs fundamentally from the bulk material response determined by means of conventional tensile and compression tests. Uchic and Dimiduk [24] demonstrated that yield strength increases by decreasing the length scale. Furthermore, as described by Broitman [25], hardness obtained by this nanoindentation method is closely related to the plastic deformation of the surface and other mechanical properties of materials such as creep strength, ductility and fatigue resistance. In the present work, the nanoindentation technique was used with the aim of identify- ing the anisotropic behavior of the Ti-6Al-4V alloy and establishing a relationship between its macroscopic and micro-/submicrometric mechanical properties. Systematic sets of tensile, compression and nanoindentation tests, performed in two orthogonal material directions, were obtained to correlate the different length scales behavior. In addition, advanced characterization techniques, such as ﬁeld-emission scanning electron microscopy, were used to investigate the plastic deformation induced at the nanometric length scale under complex stress ﬁelds.

2. Materials and Methods 2.1. Sample Preparation The material analyzed in this research was a two-phase near-alpha Ti-6Al-4V alloy. The sample had a prismatic geometry, with dimensions of 60 mm × 140 mm × 40 mm (Figure1) . Mean grain size was measured following the linear intercept method on micrographs taken with a ﬁeld-emission scanning electron microscope (FESEM), resulting in equivalent ellipsoidal grain size with a length and width of 12 ± 3 and 6 ± 2 µm, respectively. The chemical composition directly determined by energy-dispersive X-ray spectroscopy (EDS) is summarized in Table1. Before nanoindentation tests, the surface of the specimens was ground and polished using silicon carbide abrasive papers, subsequently with a diamond suspension of decreasing particle size (30, 6, 3 and 1 µm), and ﬁnalizing with a colloidal alumina suspension polishing step.

2.2. Mechanical Properties at the Macro- and Nanoscales 2.2.1. Macroscale: Tensile and Compression Tests The tensile specimens were machined following the EN 10002-1 standard, and the compression specimens were obtained following the instructions presented in [26] (see Figure2). Anisotropic effect was investigated with specimens machined from the two orthogonal directions (longitudinal direction (LD) and transversal direction (TD)) for both loading conditions. Metals 2021, 11, x FOR PEER REVIEW 3 of 19

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Figure 1. Ti-6Al-4V alloy ingot, where ST, TD and LD correspond to short transverse, transversal and longitudinal directions, respectively.

Table 1. Chemical composition of the studied Ti-6Al-4V alloy (wt.%).

Al V Fe N O C Ti 6.1 4.0 0.3 0.05 0.2 0.08 Bal.

2.2. Mechanical Properties at the Macro- and Nanoscales

2.2.1. Macroscale: TensileFigure 1.andTi-6Al-4V Compression alloy ingot, Tests where ST, TD and LD correspond to short transverse, transversal The tensile specimensand longitudinal were directions,machined respectively. following the EN 10002-1 standard, and the

compression specimensTable 1.wereChemical obtained composition followin of the studiedg the Ti-6Al-4Vinstructions alloy (wt.%). presented in [26] (see Figure 2). Anisotropic effect was investigated with specimens machined from the two orthogonal directions (longitudinalAl direction V (LD) Fe and transversal N direction O (TD)) C for both Ti loading conditions. 6.1 4.0 0.3 0.05 0.2 0.08 Bal.

Figure 2. Schematic representation of the different specimens used in the macroscopic tests. (a) Tensile and (b) compression Figure 2. Schematic representation of the different specimens used in the macroscopic tests. (a) specimens. σy and X denote the direction of the stress and the displacement associated with the tensile and compressive Tensile and (b) compression specimens. σy and X denote the direction of the stress and the dis- loadings. The positive and negative signs of the displacements correspond to the lengthening and shortening of the gauge length,placement respectively. associated with the tensile and compressive loadings. The positive and negative signs of the displacements correspond to the lengthening and shortening of the gauge length, respectively. Quasistatic uniaxial tensile tests were performed with a constant true elastoplastic strain rate of 1 × 10−3 s−1 at room temperature, following the methodology proposed Quasistatic uniaxialin [27]. tensile A Zwick tests uniaxial were electromechanical performed with testing a constant machine equippedtrue elastoplastic with a MultiSens light extensometer was used. As is well known, some mechanical properties are sensitive to −3 −1 strain rate of 1 × 10 thes strainat room rate temperature, employed to conduct following the tests. the In methodology this sense, the difference proposed in strainin [27]. rates be- A Zwick uniaxial electromechanicaltween the performed testing macroscopic machine and nanoindentation equipped with tests a MultiSens leads to negligible light variationsex- tensometer was used.in theAs computationis well known, of the some mechanical mechanical properties. properties According are to previous sensitive tests to performed the −1 strain rate employedin to these conduct specimens the [ 2tests.,17], the In average this sense, indentation the difference strain rate ofin 0.05 strain s producesrates be- a yield strength and elastic modulus slightly higher than those reported by around 2%. This error tween the performed macroscopic and nanoindentation tests leads to negligible variations could be avoided by selecting a strain rate equal to 10−3 s−1 for the nanoindentation tests. in the computation However,of the mechanical this is not straightforward properties. sinceAccording an accurate to previous material model tests is performed required due to the

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lack of homogeneity caused by the induced triaxial strains in the deformed material. Com- pression tests were performed with a servohydraulic testing machine (Schenck Hydropuls), and an optical system allowed determining the evolving loading area to compute more accurate stress [28]. Both types of experiments were performed under the displacement control mode. A minimum of three samples were tested per condition and direction in order to reveal standard deviations of mechanical properties. The uniaxial true tensile strain was measured using an extensometer until a strain level of 0.1 was reached. Furthermore, the optical measurement system was coupled in the experimental set-up in order to compute the hardening rate until a true strain of 0.43 was reached.

2.2.2. Nanoscale: Nanoindentation Tests Mechanical characterization of the Ti-6Al-4V alloy included the evaluation of its effective hardness (H) and elastic modulus (E) through the instrumented indentation technique. Nanoindentation tests were performed on a nanoindenter XP (MTS) for experiments performed at 2000 nm of maximum displacement into the surface, and the experiments 700 nm were performed with iNano equipment (Nanomechanics, Inc., Oak Ridge, TN, USA). Both nanoindenters are equipped with a continuous stiffness measurement module, allowing a dynamic determination of the mechanical properties, such as hardness and elastic modulus, during the indentation process. A Berkovich tip was used, and experimental data were analyzed using the Oliver and Pharr method [29,30]. Calibration of the contact area of the tip was performed with fused silica (known value of Young’s modulus of 72 GPa and Poisson’s ratio of 0.17 [29]). Along the indentation process, the indentation strain rate was held at 0.05 s−1. Two different sets of experiments, at the micro- and nanometric length scale, were performed under the displacement loading mode. The mechanical response of the polycrystalline alloy was assessed as the average behavior of 25 imprints (5 × 5), performed at 2000 nm of the maximum displacement into the surface or until reaching the maximum applied load of 650 mN. A constant distance of 25 µm between imprints was held in order to avoid any overlapping effect. On the other hand, to evaluate the intrinsic mechanical properties for the α-phase, homogeneous indentation arrays of 16 imprints (4 × 4) were performed in ﬁve different zones at 700 nm of maximum displacement into the surface, which implies a maximum applied load of around 50 mN. Again, a distance of about 25 µm was kept from other indentations.

2.3. Surface Assessment Deformation evolution induced during the nanoindentation process was observed using two devices: a focused ion beam (FIB) using a dual beam (FIB)/ﬁeld-emission scanning electron microscope (Carl Zeiss Neon 40, Oberkochen, Germany) operating at 20 kV for residual imprints at 2000 nm, and a scanning electron microscope Su 3500 (Hitachi, Tokyo, Japan) for 700 nm imprints.

3. Results and Discussion 3.1. Microstructure The microstructure of the studied Ti-6Al-4V alloy consists of primary, hexagonal, closely packed (hcp) α-grains embedded in a bi-phased matrix, as depicted in Figure3. The matrix is composed of alternating lamellae of a primary α-phase and body-centered cubic (bcc) β-phase. Here, the α-phase appears in gray, and the β-phase appears in white. The phases’ proportions were quantiﬁed using ﬁve different FESEM micrographs randomly recorded, with the α-phase found in 94% of the area and the β-phase in the rest. Metals 2021, 11, x FOR PEER REVIEW 5 of 19

Metals 2021, 11, 104 The phases’ proportions were quantified using five different FESEM micrographs5 of 19 randomly recorded, with the α-phase found in 94% of the area and the β-phase in the rest.

FigureFigure 3. 3.FESEM FESEM micrograph micrograph view view of the of Ti-6Al-4V the Ti-6Al-4V alloy showing alloy theshowing heterogeneous the heterogeneous distribution of distribution theof theα-/ βα-phases.-/β-phases. 3.2. Tensile and Compression Properties 3.2. Tensile and Compression Properties The true stress (σ)–true strain (ε) curves for all the studied conditions are presented in FigureThe4 a,true and stress the postprocessed (σ)–true strain data (ε are) curves summarized for all in the Table studied2. It is conditions necessary to are presented mentionin Figure that 4a, the and Young’s the moduluspostprocessed was determined data are from summarized the elastic part in Table of the σ2.–ε Itcurve is necessary to inmention the range that of 50–95%the Young’s of the elasticmodulus limit. was From determined the summarized from data, the itelastic can be part seen of that the σ–ε curve thein the yield range strength of 50–95% and the of total the elongation elastic limit. for the From specimens the summarized under study data, are strongly it can be seen that dependent on the loading stress induced in the specimen, with the values reported being higherthe yield when strength the specimen and the is deformed total elongation under compression. for the specimens Furthermore, under these study curves are strongly revealdependent that the on yield the strength loading determined, stress induced though in the the compressive specimen, loading with isthe slightly values higher reported being thanhigher those when determined the specimen under tensile is deformed loading stress,unde aroundr compression. 4.42 and 11.5%Furthe forrmore, the LD these curves andreveal TD directions,that the yield respectively. strength According determined, to the observedthough the behavior, compressive the alloy studiedloading is slightly presentshigher anthan anisotropic those determined yielding and under anisotropic tensile hardening loading effect, stress, with around a higher 4.42 yield and in the 11.5% for the TD direction than the LD direction. Furthermore, as shown in Figure4a, during uniaxial LD and TD directions, respectively. According to the observed behavior, the alloy studied loading, the initial hardening rate is always higher in compression than in tension, as reportedpresents in an [31 anisotropic–33]. On the otheryielding hand, and from anisotro the strain-hardeningpic hardening rate, effect, as a function with ofa thehigher yield in ﬂowthe TD stress direction (Figure4 b),than the the related LD deformationdirection. Furt processhermore, induced as under shown different in Figure loading 4a, during uni- stressesaxial loading, can be extracted, the initial primarily hardening in terms rate of is dislocations. always higher Here, in only compression two stages (I than and in tension, II)as appear.reported Stage in [31–33]. I is based On on dipolethe other trapping, hand, which from results the strain-hardening from edge dislocations rate, ofas aa function of singlethe flow Burgers stress vector (Figure of opposite 4b), the signs, related inducing deformation a gliding process process on induced parallel planes under and, different load- and a result, inducing an attractive force [34]. Stage II is most easily understood in terms Metals 2021, 11, x FOR PEER REVIEW ing stresses can be extracted, primarily in terms of dislocations. Here, only7 oftwo 19 stages (I of a real glide, whereby dislocation loops expand across the slip plane and deposit loops aroundand II) local appear. hard spotsStage [ 35I is]. based on dipole trapping, which results from edge dislocations of a single Burgers vector of opposite signs, inducing a gliding process on parallel planes and, and a result, inducing an attractive force [34]. Stage II is most easily understood in terms of a real glide, whereby dislocation loops expand across the slip plane and deposit loops around local hard spots [35]. As shown in Table 2, the elastic-to-plastic transition determined from the tensile and compressive stress–strain curves of the investigated Ti-6Al-4V alloy (Figure 4a) exhibits significant differences in the initial yielding stress value. However, as shown in Figure 4b, the strain-hardening rate exhibits a similar behavior within Stages I and II. This representation highlights the yielding asymmetry effect between tension and compression, generally known as the strength differential effect (SDE), a phenomenon mainly characterized at different strains or plastic work levels. The mechanical properties summarized in Table 2 show a strong anisotropic effect, as reported in previous works [10,12,15,17].

Figure 4. Cont.

Figure 4. (a) True stress vs. true strain representation and (b) strain-hardening rate vs. flow stress for the tensile and compression tests performed in two different orthogonal directions (LD and TD).

The strain-hardening behavior of metals is mainly dictated by the ability of defects to rearrange into energy-minimizing structures, as widely investigated [36]. The most commonly used strength models were developed to capture strain-hardening behavior due to the reorganization of dislocation networks. Some models employ a parabolic [37,38] or exponential function [39] to capture the transition from linear hardening to dynamic recovery [38], which can be physically connected to the evolution of dislocation populations [40–44]. Within this context, and from the experimental values of stress–strain under tension and compression, the strain-hardening exponent (n) is determined considering the well-known Hollomon power law relationship [45]. Figure 5 shows a log-log representation of true stress and true plastic strain, showing the presence of two different n exponents at a similar plastic strain threshold of 1.83% for all the investigated specimens. The two different distinguished regions are as follows:

Region 1: from 0 ≤ εp (%) ≤ 1.83 (denoted as nR1);

Region 2: from 1.83 ≤ εp (%) ≤ 9 (denoted as nR2). The strain-hardening exponent as well as the fitting R2 coefficients of the power law relationship for each region are given in Table 3. The higher value of the n exponent found under compressive loadings highlights the distortional hardening behavior. The different values in the orthogonal directions evidence the presence of anisotropic strain hardening in the Ti-6Al-4V alloy.

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FigureFigure 4. 4. (a(a)) True True stress vs.vs. truetrue strain strain representation representation and and (b) ( strain-hardeningb) strain-hardening rate vs.rate ﬂow vs. flow stress stress for forthe the tensile tensile and and compression compression tests tests performed performed in two in differenttwo different orthogonal orthogonal directions directions (LD and (LD TD). and TD). As shown in Table2, the elastic-to-plastic transition determined from the tensile and compressive stress–strain curves of the investigated Ti-6Al-4V alloy (Figure4a) exhibits signiﬁcantThe strain-hardening differences in the behavior initial yielding of metals stress is value.mainly However, dictated asby shown the ability in Figure of defects4b, tothe rearrange strain-hardening into energy-minimizing rate exhibits a similar structur behaviores, withinas widely Stages investigated I and II. This [36]. representa- The most commonlytion highlights used the strength yielding models asymmetry were effect develop betweened to tension capture and strain-hardening compression, generally behavior dueknown to the as thereorganization strength differential of dislocation effect (SDE), networks. a phenomenon Some models mainly employ characterized a parabolic at [37,38]different or strainsexponential or plastic function work [39] levels. to captur The mechanicale the transition properties from summarized linear hardening in Table to2 dy- namicshow arecovery strong anisotropic [38], which effect, can asbe reported physically in previous connected works to the [10 ,12evolution,15,17]. of dislocation populationsThe strain-hardening [40–44]. Within behavior this context, of metals and from is mainly the experimental dictated by the values ability of ofstress–strain defects underto rearrange tension into and energy-minimizingcompression, the strain-har structures,dening as widely exponent investigated (n) is determined [36]. The most consid- commonly used strength models were developed to capture strain-hardening behavior ering the well-known Hollomon power law relationship [45]. Figure 5 shows a log-log due to the reorganization of dislocation networks. Some models employ a parabolic [37,38] representation of true stress and true plastic strain, showing the presence of two different or exponential function [39] to capture the transition from linear hardening to dynamic nrecovery exponents [38 at], whicha similar can plastic be physically strain threshol connectedd of to1.83% the evolutionfor all the ofinvestigated dislocation specimens. popula- Thetions two [40 different–44]. Within distinguis this context,hed regions and from are the as experimental follows: values of stress–strain under Regiontension 1: and from compression, 0 ≤ εp (%) the≤ 1.83 strain-hardening (denoted as n exponentR1); (n) is determined considering the well-known Hollomonε power law relationship [45]. Figure5 shows a log-log representation Regionof true 2: stress from and 1.83 true ≤ p plastic (%) ≤ strain,9 (denoted showing as nR2 the). presence of two different n exponents at aThe similar strain-hardening plastic strain threshold exponent of as 1.83% well foras the all thefitting investigated R2 coefficients specimens. of the Thepower two law relationshipdifferent distinguished for each region regions are aregiven as follows:in Table 3. The higher value of the n exponent found

underRegion compressive 1: from 0 ≤ loadingsεp (%) ≤ 1.83 highlights (denoted the as di nstortionalR1); hardening behavior. The different valuesRegion in 2: the from orthogonal 1.83 ≤ εp (%)directions≤ 9 (denoted evidence as n theR2). presence of anisotropic strain hardening in theThe Ti-6Al-4V strain-hardening alloy. exponent as well as the ﬁtting R2 coefﬁcients of the power law relationship for each region are given in Table3. The higher value of the n exponent found under compressive loadings highlights the distortional hardening behavior. The different values in the orthogonal directions evidence the presence of anisotropic strain hardening in the Ti-6Al-4V alloy.

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Table 2. Summary of the mechanical properties directly determined from the true stress–true strain curve presented in Figure4a.

Ultimate Orthogonal Young’s Initial Yield Global Testing Strain, Rate, Tensile Uniform True Fracture True Stress at Material . Modulus, Strength, Hardening Loading ε S−1 Strength, Elongation, ε Strain, ε Fracture MPa Direction E (GPa) σ (MPa) u Exponent, n f 0.2% UTS (MPa) LD 0.001 111 ± 1 927 ± 3 951 0.10 0.045 0.41 1241 Tension TD 0.001 115 ± 4 933 ± 1 982 0.97 0.043 0.40 1349 LD 0.001 122 ± 1 968 ± 3 - - 0.052 - - Compression TD 0.001 128 ± 3 1040 ± 6 - - 0.059 - -

Note: Due to the experimental set-up, the UTS, εu, εf and true stress at fracture were not possible to acquire for the compression tests. Metals 2021, 11, x FOR PEER REVIEW 8 of 19 Metals 2021, 11, x FOR PEER REVIEW 8 of 19 Metals 2021, 11, 104 8 of 19

Figure 5. Log-log representation of true stress (ln σ) and true plastic strain (ln εp). Range of interest: 0% ≤ εp ≤ 9%. Figure 5.5.Log-log Log-log representation representation of trueof true stress stress (ln σ (ln) and σ) trueand plastic true plastic strain (lnstrainεp). Range(ln εp). of Range interest: of interest:0% ≤0%εp ≤≤ ε9%.p ≤ 9%. Table 3. Summary of the strain-hardening exponents of the power law relationship determined in both regions with their respective fitting coefficients R2. nR1 and nR2 denote the n exponent for each region present in Figure 5. TableTable 3. 3.SummarySummary of of the the strain-hardening exponents exponents of theof the power power law la relationshipw relationship determined determined in both in regions both regions with their with their 2 respectiveLoadingrespective fitting fitting coefficientsMaterial coefficients RR2.. nnR1R1 and nnR2R2 denotedenote the the n n exponent exponent for for each each region region present present in Figure in Figure5. 5. nR1 (−) nR2 (−) R2R1 (−) R2R2 (−) Stress Direction 2 2 Loading Stress Material Direction nR1 (−) nR2 (−) R R1 (−) R R2 (−) Loading Material −2 −4 −2 −4 LD 2.77 × 10 n ±R 9.451 (−) × 10 5.86 × 10 ± 9.03nR2 (×− 10) 0.966 R2R1 (−0.987) R2R2 (−) T LD 2.77 × 10−2 ± 9.45 × 10−4 5.86 × 10−2 ± 9.03 × 10−4 0.966 0.987 StressT DirectionTD 2.81 × 10−2 ± 4.68 × 10−4 6.13 × 10−2 ± 3.96 × 10−4 0.986 0.993 TD 2.81 × 10−2 ± 4.68 × 10−4 6.13 × 10−2 ± 3.96 × 10−4 0.986 0.993 LDLD 2.95 2.77 × ×10 10−2 ±−2 2.48± 9.45 × 10 ×− 104 −4 7.71 5.86× 10 −×2 ±10 4.36−2 ± × 9.03 10−4 × 10−4 0.995 0.966 0.987 0.987 T C LD 2.95 × 10−2 ± 2.48 × 10−4 7.71 × 10−2 ± 4.36 × 10−4 0.995 0.987 C TDTD 4.16 2.81 × ×10 10−2 ±−2 1.08± 4.68 × 10 ×− 104 −4 7.99 6.13× 10 −×2 ±10 2.49−2 ± × 3.96 10−4 × 10−4 0.999 0.986 0.994 0.993 TD 4.16 × 10−2 ± 1.08 × 10−4 7.99 × 10−2 ± 2.49 × 10−4 0.999 0.994 LD 2.95 × 10−2 ± 2.48 × 10−4 7.71 × 10−2 ± 4.36 × 10−4 0.995 0.987 C 3.3. Micro- and Nanomechanical−2 Properties−4 −2 −4 TD 3.3. Micro- 4.16 and × 10 Nanomechanical ± 1.08 × 10 Properties 7.99 × 10 ± 2.49 × 10 0.999 0.994 3.3.1. Loading/Unloading Curve 3.3.1. Loading/Unloading Curve 3.3. Micro-Typical andloading–displacement Nanomechanical Properties (P–h) curves generated with the Berkovich indenter Typical loading–displacement (P–h) curves generated with the Berkovich indenter into the surface for monotonic loading performed under the displacement control mode 3.3.1.into the Loading/Unloading surface for monotonic Curve loading performed under the displacement control mode are shown in Figure 6 for the LD and TD directions. The P–h curve for the LD direction are shown in Figure6 for the LD and TD directions. The P–h curve for the LD direction exhibitsTypical the lowest loading–displacement applied load under maxi(P–h)mum curves displacement generated into with the thesurface Berkovich after the indenter exhibits the lowest applied load under maximum displacement into the surface after the indenterinto the issurface withdrawn, for monotonic confirming loading that this performed direction is undersofter than the displacementTD and pointing control out mode indenter is withdrawn, confirming that this direction is softer than TD and pointing out theare strong shown anisotropy in Figure effect 6 for of the the LD Ti-6Al-4V and TD alloy. directions. No discontinuities The P–h curve during for the the loading LD direction the strong anisotropy effect of the Ti-6Al-4V alloy. No discontinuities during the loading curve could be detected for the LD and TD directions. exhibitscurve could the belowest detected applied for the load LD andunder TD maxi directions.mum displacement into the surface after the indenter is withdrawn, confirming that this direction is softer than TD and pointing out the strong anisotropy effect of the Ti-6Al-4V alloy. No discontinuities during the loading curve could be detected for the LD and TD directions.

FigureFigure 6. 6. LoadingLoading curves curves for for both both the the orthogonal orthogonal directions directions investigated investigated here here (LD (LD and and TD). TD).

Figure 6. Loading curves for both the orthogonal directions investigated here (LD and TD).

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3.3.2. Mechanical Properties of the Ti-6Al-4V Alloy from Nanoindentation 3.3.2. Mechanical Properties of the Ti-6Al-4V Alloy from Nanoindentation A continuous computation of hardness and elastic modulus as a function of the max- A continuous computation of hardness and elastic modulus as a function of the imum displacement into the surface of the polycrystalline alloy are shown in Figure 7. As maximum displacement into the surface of the polycrystalline alloy are shown in Figure7. appreciated,As appreciated, the behavior the behavior of the of indented the indented material material is affected is affected by bythe the penetration penetration depth. depth. ForFor indents indents shallower shallower than than 200 200 nm, nm, hardness hardness and andelastic elastic modulus modulus values values are strongly are strongly af- fectedaffected by length by length scale scale or indentation or indentation size size effect effects.s. However, However, these these values values tend tend to tostabilize, stabilize, withinwithin the the experimental experimental error error range, range, as as the the penetration penetration depth depth increases increases beyond beyond 200 200 nm. nm.

FigureFigure 7. 7.MicromechanicalMicromechanical properties: properties: (a) (hardnessa) hardness and and (b) (elasticb) elastic modulus modulus vs. vs.displacement displacement into into thethe surface; surface; a function a function of ofthe the loading loading directio directionn (LD (LD and and TD TD in inblack black and and blue, blue, respectively). respectively).

HardnessHardness and and elastic elastic modulus modulus values values obtained obtained as as an an average in the stabilizedstabilized zonezone at at thethe micrometricmicrometric lengthlength scalescale forfor thethe LDLD andand TDTD areare summarizedsummarized inin TableTable4 .4. The The Ti-6Al-4V Ti-6Al- 4Valloy alloy found found to beto stronglybe strongly anisotropic anisotropic due due to the toα -phasethe α-phase at room at temperatureroom temperature is strongly is stronglyanisotropic anisotropic at thesingle at the crystalsingle crystal level, as leve reportedl, as reported by [46], by which [46], dependswhich depends on the materialon the materialdirection, direction, in terms in of terms hardness of hardness and elastic and modulus,elastic modulus, with the with TD orientationthe TD orientation being harder be- ingand harder stiffer and than stiffer the than LD. Thisthe LD. trend This may tren bed associatedmay be associated with the with interacting the interacting deformation de- formationmechanisms. mechanisms. The reported The reported hardness hardness for both orthogonalfor both orthogonal directions directions is in fair agreementis in fair with the indentation hardness determined through the ﬁnite-element approach [47]. Fur-

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thermore, the reported hardness obtained by the nanoindentation method is in accordance with previous references, where Han et al. [48] reported a hardness value of the Ti-6Al-4V alloy ranging between 4.09 and 4.71 GPa, and Li et al. [49] found a relative hardness value of around 4.1–5.0 Gpa. Cai et al. [50] reported a hardness value at the micrometric length scale by means of microindentation, which varied from 4.0 to 5.5 Gpa depending on the indentation depth. Babu and coworkers [51] investigated micromechanical properties as a function of the strain rate and found a hardness value ranging between 4.26 and 4.40 GPa for strain rates of 0.05 and 0.20 s−1.

Table 4. Summary of the mechanical properties (hardness, elastic modulus and ﬂow stress) determined using the nanoindentation technique and obtained as an average from the stabilized zone for the commercial Ti-6Al-4V alloy as a function of the material direction.

Material Direction H (GPa) E (GPa) σf ﬂow (GPa) LD 3.6 ± 0.2 125 ± 2 1.3 ± 0.1 TD 4.5 ± 0.5 151 ± 9 1.7 ± 0.2

The values of the elastic modulus are slightly greater than those determined at the macroscopic length scale (Table1). This discrepancy could be mainly attributed to the fact that Oliver and Pharr’s method based on Sneddon’s analysis of elastic contact, as employed here, considers that the effective elastic modulus (Eeff) is only affected by the material elastic moduli in the indentation direction and, therefore, does not take into account any of the lateral stresses generated during the indentation process. This stress process produces an overestimation of the elastic modulus through the β parameter, presented in the following equation [10,52]: √ 1 π S Ee f f = p (1) β 2 A(hc) where β is equal to 1.034 for a Berkovich indenter [53], S is the contact stiffness and A(hc) is the contact area. It is necessary to highlight that this overestimation does not affect the discussion of the results because all values are equally overestimated. Wen et al. [21], using a spherical indenter at the micrometric length scale, also reported an elastic modulus around 38% higher than the original elastic modulus tested by the conventional stress–strain method. This trend is in fair agreement with the obtained results in both orthogonal directions, summarized in Table4. Furthermore, the data obtained in this manuscript are around 4 and 25% higher for the LD and TD directions, respectively, than those reported at 2000 nm of maximum displacement into the surface by Babu et al. [47]. One of the key parameters to take into consideration for conducting finite-element modeling (FEM) is the flow stress (σflow), a critical parameter for reliable evaluation of the energy expended in the flow and fracture. In this sense, this parameter was calculated through the simple convention of previously estimated hardness data. Accordingly, σflow was reported as the ratio between the measured Vickers hardness (HV) and a constraint factor (ψ), commonly taken as three for soft, ductile metals. A correction factor of 0.9 in ψ was applied, related to the consideration of the Berkovich indenter geometry instead of a Vickers geometry, as reported in [54]. The σflow for both directions is summarized in Table4, yielding an upper and lower limit of 1.7 ± 0.2 and 1.3 ± 0.1 GPa for the TD and LD directions, respectively. The σflow determined by combining the indentation hardness and Tabor’s equation is in fair agreement with those reported by Babu et al. [39], who reported a value of 1.12 GPa at a constant strain rate of 0.2 s−1. Furthermore, these values are in concordance with those reported by Kumaraswamy et al. [55], determined under compressive flow stress at average strains ranging between 4% and 7%. Metals 2021, 11, x FOR PEER REVIEW 11 of 19

Metals 2021, 11, 104 concordance with those reported by Kumaraswamy et al. [55], determined under com-11 of 19 pressive flow stress at average strains ranging between 4% and 7%.

3.3.3. Anisotropy Effect 3.3.3. Anisotropy Effect Once the anisotropy effect was demonstrated, a detailed analysis was performed by Once the anisotropy effect was demonstrated, a detailed analysis was performed by making residual imprints at 700 nm of maximum displacement into the surface in order making residual imprints at 700 nm of maximum displacement into the surface in order to to confine the stress field mainly inside the α-grains. Figure 8 presents typical indentation confine the stress field mainly inside the α-grains. Figure8 presents typical indentation loading–unloading curves for single indentations performed randomly under a loading loading–unloading curves for single indentations performed randomly under a loading control mode of 50 mN. A broad dispersion of P–h curves could be distinguished for both control mode of 50 mN. A broad dispersion of P–h curves could be distinguished for both orthogonal directions investigated here (LD and TD directions depicted in Figure 8a,b, orthogonal directions investigated here (LD and TD directions depicted in Figure8a,b, respectively). The curves with smaller depth values correspond to indentations made in respectively). The curves with smaller depth values correspond to indentations made in the - theα-phase α phase region, region, whereas whereas the the set set of curvesof curves with with higher higher depths depths are attributedare attributed to indentations to inden- tationsmade made at the atα-/ theβ-phases, α-/β-phases, as represented as represented in Figure in Figure9 (an example9 (an example is denoted is denoted in this in figure this figurewith with a white a white dashed dashed circle). circle).

FigureFigure 8. 8.IndentationIndentation loading–unloading loading–unloading curves curves (or (or P–h P–h curves) curves) performed performed at at50 50mN mN of ofmaximum maximum appliedapplied load load for for the the (a ()a LD) LD and and (b ()b TD) TD directions directions of of the the Ti-6Al-4V Ti-6Al-4V alloys. alloys.

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FigureFigure 9. 9.SEM SEM micrograph micrograph of of one one array array of imprintsof imprints performed performed under under the displacementthe displacement control control mode mode at 700 at nm 700 of nm maximum of maxi- penetrationmum penetration depth. Thedepth. white The dashed white circledashed denotes circle andenote examples an example of a residual of a imprintresidual performed imprint performed at the α-/ βat-interphase. the α-/β-interphase. Furthermore, from the qualitative observation of the P–h curves depicted in Figure8, it is possibleFurthermore, to discern from that the the qualitativeα-phase is observation harder than of the the zones P–h withcurvesα-/ depictedβ-lamellas. in Figure This finding8, it is possible highlights to discern that the thatβ-phase the α-phase is softer is thanharder the thanα-phase. the zones A similar with α observation-/β-lamellas. hasThis beenfinding reported highlights in the that literature the β-phase [42,56 ].is Moreover,softer than as the can α- bephase. seen A in similar the unloading observation curves has ofbeen Figure reported8, from in the the final literature penetration [42,56]. depth More (seeover, * inas Figurecan be8 ),seen the inα the-phase unloading for the TDcurves is slightlyof Figure harder 8, from than the for final the LD penetration direction. depth The results (see * extracted in Figure from 8), the these α-phase curves for confirmed the TD is theslightly anisotropic harder behavior than for as the a function LD direction. of hardness The results of the Ti-6Al-4Vextracted alloyfrom in these both curves directions, con- withfirmed the the obtained anisotropic results behavior for the α -phaseas a function being inof fairhardness agreement of the with Ti-6Al-4V those summarized alloy in both indirections, Table4. with the obtained results for the α-phase being in fair agreement with those summarizedFigure 10 inshows Table the 4. elastic modulus histograms with a 2 GPa bin size, determined from 64Figure indents 10 shows per each the orthogonal elastic modulus direction. histograms A monomodal with a 2 peak GPa centeredbin size, atdetermined 109 and 119from GPa 64 for indents the LD per and each TD orthogonal directions, respectively,direction. A couldmonomodal be observed. peak centered The graphs at 109 clearly and show119 GPa that for the the TD LD direction and TD is directions, stiffer than respecti the LDvely, direction, could with be observed. this trend The and graphs these elastic clearly modulusshow that values the TD being direction in good is stiffer agreement than the with LD direction, those obtained with this by trend conventional and these tensile elastic testsmodulus in the values Ti-6Al-4V being alloy, in good summarized agreement in with Table those2[ 7]. obtained They are by also conventional in concordance tensile withtests those in the reported Ti-6Al-4V by alloy, Kherrouba summarized et al. in [57 Table]. The 2 [7]. elastic They modulus are also valuesin concordance reported with in Figurethose reported10 are between by Kherrouba 15% and et al. 26% [57]. lower, The el forastic the modulus LD and values TD orthogonal reported in directions, Figure 10 respectively,are between than15% thoseand 26% obtained lower, at for maximum the LD an displacementd TD orthogonal into directions, the surface respectively, of around 2000than nm those (see obtained Table4 and at Figure maximum7a). This displacement difference mayinto bethe associated surface of with around the fact 2000 that nm data (see presented in Figure 10 come from tests mainly performed in the α-phase and some of them Table 4 and Figure 7a). This difference may be associated with the fact that data presented at the interface between the α-/β-phase. This observation points out that both phases are in Figure 10 come from tests mainly performed in the α-phase and some of them at the anisotropic in terms of hardness. As shown in Figure9, when the residual imprint as well interface between the α-/β-phase. This observation points out that both phases are aniso- as the plastic flow induced during the indentation process interact with the β-phase, the tropic in terms of hardness. As shown in Figure 9, when the residual imprint as well as P–h curve moves to higher displacement into the surfaces (see Figure8 ), highlighting that the plastic flow induced during the indentation process interact with the β-phase, the P– the mechanical behavior of the α-/β-interphase is softer than the mechanical behavior for h curve moves to higher displacement into the surfaces (see Figure 8), highlighting that the α-phase. A similar trend has been observed for the elastic modulus, where the α-phase the mechanical behavior of the α-/β-interphase is softer than the mechanical behavior for is stiffer, which is determined by the modulus of the individual phases and their volume the α-phase. A similar trend has been observed for the elastic modulus, where the α-phase fractions as reported by Hao et al. [58], and more sensitive to phase/crystal structure than is stiffer, which is determined by the modulus of the individual phases and their volume other factors [59]. fractions as reported by Hao et al. [58], and more sensitive to phase/crystal structure than other factors [59].

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Figure 10. Elastic modulus histograms determined from 64 indents performed at constant displace- mentFigure into the10. surface Elastic of 700 modulus nm for both orthogonalhistograms directions determined (LD and TD). from 64 indents performed at constant dis- 3.3.4.placement Deformation into Mechanisms the surface Induced of 700 by Nanoindentation nm for both orthogonal directions (LD and TD). Figure 11 shows a FESEM image corresponding to a homogeneous array of imprints performed3.3.4. Deformation at a penetration depth Mechanisms of 2000 nm. Among induced the numerous by Nanoindentation possible deformation processes encountered in hexagonal, closely packed metals, slip is the main deformation systemFigure of the α-phase 11 shows at room temperature, a FESEM as image appreciated corresponding around the indents shownto a homogeneous in array of imprints Figure 11a. It is clear that the plastic deformation field generated during nanoindentation isperformed confined under at the a imprintpenetration interacting depth with several of 2000 grains. nm. A close Among inspection the of some numerous possible deformation residualprocesses imprints encountered is shown in Figure in 11hexagonal,b,c, and no plastic closely deformation packed induced metals, can be slip is the main deformation observed. This can be due to the fact that the particular crystallographic orientation is not favorablesystem to of activate the α slip-phase traces and at alsoroom to the temperature, high amount of β-phase, as appr as observedeciated in around the indents shown in Figure3, in 11a. the indented It is clear zone, which that blocks the theplastic activation defo and emergencermation of field the slip generated traces during nanoindentation until reaching the surface. The location of these imprints in a region with a high amount ofis βconfined-phase implies under that higher the stress imprint is required interacting to induce slip with traces asseveral well as twining. grains. A close inspection of some Onresidual the other imprints hand, in Figure is 11 shownd, the plastic in fieldFigure induced 11b,c, by nanoindentations and no plastic may be deformation induced can be observed around the residual imprint. Furthermore, two transformation twins at the edge ofobserved. the residual imprintThis can (marked be with due a whiteto the arrow fact in Figure that 11thed) with particular a lenticular shapecrystallographic orientation is not canfavorable be seen. Unlike to activate slip, twinning slip depends traces not justand on thealso resolved to the shear high stress amount but also of β-phase, as observed in on its sign. In polycrystalline materials, deformation behavior is mainly governed by the Figure 3, in the indented zone, which blocks the activation and emergence of the slip traces until reaching the surface. The location of these imprints in a region with a high amount of β-phase implies that higher stress is required to induce slip traces as well as twining. On the other hand, in Figure 11d, the plastic field induced by nanoindentations may be observed around the residual imprint. Furthermore, two transformation twins at the edge of the residual imprint (marked with a white arrow in Figure 11d) with a lenticular shape can be seen. Unlike slip, twinning depends not just on the resolved shear stress but also on its sign. In polycrystalline materials, deformation behavior is mainly governed by the relative activation of the different deformation mechanisms and their interactions, which strongly depend on the crystallographic texture and deformation mode and, therefore, are difficult to predict.

Metals 2021, 11, 104 14 of 19

Metals 2021, 11, x FOR PEER REVIEW relative activation of the different deformation mechanisms and their interactions, which 14 of 19 strongly depend on the crystallographic texture and deformation mode and, therefore, are difﬁcult to predict.

Figure 11. a b d Figure 11. FESEMFESEM micrographs micrographs showing showing the the residual residual imprints. ( ()a General) General view view of the of array the array of the residualof the residual imprints; imprints; ( – ) (b– FESEM magnifications of some residual imprints in order to show the different deformation features. d) FESEM magnifications of some residual imprints in order to show the different deformation features. Figure 12 shows a view of a residual imprint entirely embedded within the α-phase. ThisFigure will also12 shows apply fora view plastic of field a residual dimensions, imprint estimated entirely to range embedded between 4.9 within and 7.0 theµm α-phase. This(i.e., will between also apply 7 and for 10 timesplastic the field maximum dimensions, displacement estimated into the to surface), range slightly between smaller 4.9 and 7.0 µm than(i.e., thebetween mean grain 7 and size 10 experimentally times the maximu determinedm displacement for the Ti-6Al-4V intoα-phase. the surface), This fact slightly smallerindicates than that the datamean gathered grain fromsize indentationsexperimentally 700 nmdetermined in depth are for valid the forTi-6Al-4V extracting α-phase. intrinsic hardness values of this phase. Furthermore, no slip traces were observed around Thisthe fact residual indicates imprint, that which data implies gathered that thefrom crystallographic indentations orientation 700 nm in of thedepthα-phase are isvalid for extractingnot favorable intrinsic to activate hardness the slipvalues system. of this Some phase. of the residualFurthermore, imprints no are slip located traces near were ob- servedthe centeraround of αthe-grains, residual whereas imprint, others which are located implies nearer that to the the grain crystallographic boundaries or evenorientation in of the αthe-phaseβ-phase. is not In the favorable present study, to activate only nanoindents the slip system. near the Some center of of αthe-grains residual were takenimprints are locatedinto near consideration the center in order of α-grains, to minimize whereas the influence others of are grain located boundaries nearer and to the theβ -phasegrain bound- on extracted values of the constitutive hardness. Thus, a hardness value for the α-phase aries or even in the β-phase. In the present study, only nanoindents near the center of α- between 5.3 and 7.1 GPa was obtained. This significant trend may be associated with the grainsspecific were crystallographic taken into consideration orientation for in the orderα-grains, to minimize and the highest the influence hardness of value grain may boundaries beand associated the β-phase with an onα-grain extracted with a values crystallographic of the cons orientationtitutive near hardness. the [0001] Thus, stress axis,a hardness valuethe for latter the in α fair-phase agreement between with 5.3 the valuesand 7.1 reported GPa was by Viswanathan obtained. This et al. [significant60]. In addition, trend may be associatedthe hardness with value the decreases specific as crystallographic the indentation stress orientation axis induced for during the α- thegrains, indentation and the highest hardnessprocess deviates value frommay the be [0001]associated orientation with [ 47an]. α-grain with a crystallographic orientation The relationship between flow stress obtained at the macroscopic length scale under near the [0001] stress axis, the latter in fair agreement with the values reported by Viswa- different stress fields (tensile and compression) and the flow stress determined at the nathanmicrometric et al. [60]. length In addition, scale can bethe graphically hardness displayedvalue decreases using Tabor’s as the equation.indentation At thestress axis inducedmacroscopic duringlength the indentation scale, Figure process 13a represents deviates the from flow stressthe [0001] determined orientation through [47]. the compression (y-axis) and tensile tests (x-axis). Figure 13b displays the linear relationship between the compressive flow stress and the flow stress determined using the composite hardness (hardness taking into account both constitutive phases in the Ti-6Al-4V alloys, α-/β-) combined with Tabor’s equation.

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Figure 12. FESEM magnification micrograph of a specific location of a residual imprint performed Figure 12. at 700 nm of FESEMmaximum magnification displacement into micrograph the surface, where of a specificindividual location imprints ofwithin a residual the Ti- imprint performed at 7006Al-4V nm α-phase of maximum are clearly displacement appreciated (white into dashed the surface, square presented where in individual Figure 9). imprints within the Ti-6Al-4V α-phase are clearly appreciated (white dashed square presented in Figure9). 3.4. Mechanical Properties Correlation: From the Macro- to Nanometric Length Scale 3.4. MechanicalThe relationship Properties between Correlation:flow stress obtain Fromed at the the Macro- macroscopic to Nanometric length scale Lengthunder Scale different stress fields (tensile and compression) and the flow stress determined at the mi- Furthermore, under the current investigated conditions (in terms of loads, stresses, crometric length scale can be graphically displayed using Tabor’s equation. At the macro- strains,scopic length room scale, temperature Figure 13a represents and quasistatic the flow stress state), determined the flow through stress determinedthe com- at the macro- scopicpression length (y-axis) scaleand tensile under tests different (x-axis). Figure stress 13b fields displays (compression the linear relationship and/or be- tensile) can be pre- dictedtween the with compressive a simple flow nanoindentation stress and the flow test stress and determined subsequently using the using composite Tabor’s expression. In otherhardness words, (hardness if all taking the testinginto account parameters both constitutive are controlled, phases in the a simpleTi-6Al-4V predictive alloys, model can be α-/β-) combined with Tabor’s equation. obtainedFurthermore, in which under a nanoindentation the current investigated test canconditions be used (in toterms estimate of loads, both stresses, the flow stress under compressionstrains, room temperature (equation and provided quasistatic instate), Figure the flow 13 b)stress and determined tensilestresses at the macro- using the following expression:scopic length scale under different stress fields (compression and/or tensile) can be pre- dicted with a simple nanoindentation test and subsequently using Tabor’s expression. In σflow,tensile = 0.908 + 0.015·σflow,nanoindentation (2) other words, if all the testing parameters are controlled, a simple predictive model can be obtainedTaking in which into a nanoindentation account Tabor’s test equation,can be used toσflow estimate= H compositeboth the/(3 flow·ψ stress), where un- Hcomposite refers toder the compression bulk material (equation properties, provided in EquationFigure 13b) and (2) cantensile be stresses rewritten using inthe termsfollow- of the composite ing expression: nanoindentation hardness as follows: Metals 2021, 11, x FOR PEER REVIEW σflow,tensile = 0.908 + 0.015·σflow, nanoindentation (2) 16 of 19 −3 Taking into account Tabor’sσflow,tensile equation,= σ 0.908flow = Hcomposite + 5.56/(3·ψ×), 10where· Hcompositecomposite refers to the (3) bulk material properties, Equation (2) can be rewritten in terms of the composite nanoindentation hardness as follows:

σflow,tensile = 0.908 + 5.56 × 10−3·Hcomposite (3) This predictive model has a potential practical implication since by only measuring a single mechanical property, the flow stress under different deformation fields can be obtained at the macroscopic length scale, thus avoiding the machining of both tension and compression specimens (see Figure 2), of which the procedure is expensive, time and material consuming and cumbersome to perform in the industry.

Figure 13. Cont.

Figure 13. Relationship between flow stress determined under different stress fields and also at different length scales. (a) Flow stress under compression vs. under the tensile test; both tests were performed at the macroscopic length scale and (b) flow stress under compression (macroscopic length scale) vs. the one determined at the micrometric length scale using the composite indentation hardness and Tabor’s equation.

4. Conclusions Based on the obtained results for the investigated Ti-6Al-4V alloy, the following conclusions can be drawn: (1) The mechanical properties tested under different stress fields at the macroscopic length scale present different mechanical behavior, with compression being slightly higher than that obtained by tensile tests. (2) The stress–strain curves at the macroscopic length scale are strongly anisotropic depending on the testing direction, with flow stress and hardening being around 20– 25% higher for the TD direction than for the LD direction.

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FigureFigure 13. 13. RelationshipRelationship between between flow flow stress stress determined determined under under different different stress stress fields fields and andalso alsoat at differentdifferent length length scales. scales. (a ()a Flow) Flow stress stress under under compression compression vs. vs. under under the the tensile tensile test; test; both both tests tests were were performedperformed at atthe the macroscopic macroscopic length length scale scale and and (b) (flowb) flow stress stress under under compression compression (macroscopic (macroscopic lengthlength scale) scale) vs. vs. the the one one determin determineded at at the the micrometric micrometric length length scale scale using using the the composite composite indenta- indentation tionhardness hardness and and Tabor’s Tabor’s equation. equation.

4. ConclusionsThis predictive model has a potential practical implication since by only measuring a singleBased mechanical on the obtained property, results the for flow the stressinvestigated under Ti-6Al-4V different deformation alloy, the following fields can con- be clusionsobtained can at be the drawn: macroscopic length scale, thus avoiding the machining of both tension (1)and The compression mechanical specimens properties (see tested Figure under2), of whichdifferent the stress procedure fields is at expensive, the macroscopic time and materiallength consuming scale present and different cumbersome mechanical to perform behavior, in the with industry. compression being slightly higher than that obtained by tensile tests. 4. Conclusions (2) The stress–strain curves at the macroscopic length scale are strongly anisotropic de- pendingBased onon thethe obtainedtesting direction, results forwith the flow investigated stress and Ti-6Al-4V hardening alloy, being the around following 20– conclusions25% higher can for be the drawn: TD direction than for the LD direction. (1) The mechanical properties tested under different stress fields at the macroscopic length scale present different mechanical behavior, with compression being slightly higher than that obtained by tensile tests. (2) The stress–strain curves at the macroscopic length scale are strongly anisotropic depending on the testing direction, with flow stress and hardening being around 20–25% higher for the TD direction than for the LD direction. (3) The hardness, elastic modulus and flow stress values at the submicrometric length scale for the TD direction are around 25, 21 and 32% higher than those measured for the LD direction. (4) The P–h curves for the α- and α-/β-interphase indicate that the α-phase is harder, highlighting that the β-phase may be softer than the other two constituents in the Ti-6Al-4V alloy. (5) The high amount of β-phase heterogeneously distributed in the α-phase is responsible for blocking the activation and the emergence of the slip traces until reaching the surface. (6) A simple mathematical relationship can be obtained relating the flow stress determined under different stress fields as well as at different length scales, highlighting that the values reported under tensile, compression and even nanoindentation tests are governed by the pre-existing microstructure. Metals 2021, 11, 104 17 of 19

Author Contributions: Data curation, formal analysis, investigation, writing—original draft preparation, writing—review and editing V.T., A.F.J. and J.J.R.; writing—review and editing, formal analysis C.R.-U., C.M. and G.R.; formal analysis A.Z.; project administration, conceptualization and methodology V.T., J.J.R. and A.M.M. All authors have read and agreed to the published version of the manuscript. Funding: This work was funded by ANID Fondecyt 11170002 and Spanish Ministerio de Economía y Competitividad through Grant MAT2015-70780-C4-P (MINECO/FEDER). Acknowledgments: The current study was partially supported by the Spanish Ministerio de Economía y Competitividad through (Grant MAT2015-70780-C4-P) (MINECO/FEDER) and by the Chilean Na- tional Agency for Research and Development (ANID) Fondecyt 11170002. A.F.J., V.T. and J.J.R would like to thank the University of La Frontera (Program of Researchers), Foundequip EQM EQM170220, as well as the Serra Húnter program of the Generalitat de Catalunya for financial support. Conflicts of Interest: The authors declare no conflict of interest.

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