Recent development in beta titanium alloys for biomedical Recent development in beta titanium alloys for biomedical applications applications

: β -type titanium (Ti) alloys have attracted a lot of attention as novel biomedical materials in the past decades due to their low elastic moduli and good biocompatibility. This article provides a broad and extensive review of β -type Ti alloys in terms of alloy design, preparation methods, mechanical properties, corrosion behavior, and biocompatibility. After brieﬂy introducing the development of Ti and Ti alloys for biomedical applications, this article reviews the design of β -type Ti alloys from the perspective of the molybdenum equivalency (Mo eq ) method and DV-X α molecular orbital method. Based on these methods, a considerable number of β -type Ti alloys are developed. Although β -type Ti alloys have lower elastic moduli compared with other types of Ti alloys, they still possess higher elastic moduli than human bones. Therefore, porous β -type Ti alloys with declined elastic modulus have been developed by some preparation methods, such as powder metallurgy, additive manufacture and so on. As reviewed, β -type Ti alloys have comparable or even better mechanical properties, corrosion behavior, and biocompatibility compared with other types of Ti alloys. Hence, β -type Ti alloys are the more suitable materials used as implant materials. However, there are still some problems with β -type Ti alloys, such as biological inertness. As such, summarizing the ﬁndings from the current literature, suggestions for β -type Ti alloys with bioactive coatings are proposed for the future development.


Introduction
Thanks to their excellent mechanical properties, good corrosion resistance, as well as commendable biocompatibility, titanium (Ti) and its alloys are extensively applied in various fields, especially in the biomedical field [1][2][3][4][5][6].According to their microstructures in terms of phase constituents, Ti alloys can be roughly categorized into α-type Ti alloys, (α + β)-type Ti alloys, and β-type Ti alloys.By comparing other metallic materials for biomedical applications, Ti and Ti alloys have lower density, higher specific strength, and better corrosion resistance than stainless steels and Co-Cr-based alloys [7,8].For instance, commercially pure titanium (CP-Ti), one of the α-type Ti alloys, has been used as implant materials for nearly half of a century as the first generation of Ti biomaterials [2,8,9].Initially, CP-Ti was developed to replace stainless steels and Co-Cr alloys for implants since stainless steels and Co-Cr-based alloys contain unfriendly elements, including Ni, Co, and Cr [2,10].However, some hard tissues or load-bearing connective tissues have higher requirement of mechanical properties; CP-Ti may not satisfy this requirement due to its moderate strength [11,12].To get rid of this Metals 2020, 10, 1139 2 of 29 limitation, α + β-type Ti alloys were emerged at the right moment and they generally have higher strength than α-type Ti alloys [2,10,11,13].Typically, Ti-6Al-4V (in wt.%; the same hereafter unless indicated) is the most frequently employed α + β-type Ti alloy, accounting for 50% of Ti products besides CP-Ti [14].Nevertheless, Ti-6Al-4V contains toxic V which is harmful to the human body.As such, new dual-phase Ti alloys are developed to replace Ti-6Al-4V, such as Ti-6Al-7Nb and Ti-5Al-2.5Fe[2,10,[15][16][17].For long-term implantation, α + β-type Ti alloys exhibit good performance owing to their excellent fatigue resistance and good corrosion resistance [18,19].However, Al is still a questionable element in α + β-type Ti alloys since intaking excessive Al can trigger Alzheimer's disease [20].In addition, the elastic modulus is another important factor to evaluate the availability of Ti implants.The mismatch elastic moduli between implant and human bone would result in the stress-shielding effect, which is a potential hazard to patients and results in the bone adsorption [2,21].The elastic modulus of human cortical bone is about 30 GPa, while those of Ti-6Al-7Nb and Ti-6Al-4V are about 110 GPa and 112 GPa [2,18].Therefore, the moduli of dual-phase Ti alloys are significantly higher than that of the human cortical bone.Things have come a long way since β-type Ti alloys were designed and developed.β-type Ti alloys contain higher amounts of β-stabilizers (such as Mo, Ta, and Zr) and hence have dominant β phase in the microstructure.Due to the non-toxic nature of β-stabilizers, β-type Ti alloys not only have the decreased elastic moduli but also possess improved biocompatibility compared with other types of Ti alloys [22][23][24].For instance, the elastic modulus of Ti-24Nb-4Zr-8Sn is about 46-55 GPa [25], which is significantly lower than those of dual-phase Ti alloys.Therefore, β-type Ti alloys have a significantly important position in the biomedical field.
Up to date, biomedical β-type Ti alloys have been developed for over thirty years.Therefore, this review aims to give an overall comprehension of biomedical β-type Ti alloys.In this review, an introduction to the development of biomedical Ti and Ti alloys is first presented.As such, the significance of β-type Ti alloys can be understood.Afterward, the alloy design Metals 2020, 10, 1139 3 of 29 and processing of β-type Ti alloys are briefly introduced to know how to obtain Ti alloys with a body-centered cubic (BCC) structure at room temperature.With the development of preparation methods, new techniques, such as additively manufacturing, porous powder metallurgy and FAST-forge technology (field-assisted sintering technology, followed by forging), provide brand new ways to produce porous β-type Ti alloys with lower elastic moduli compared with the bulk counterparts.Such techniques shed insight into the preparation of β-type Ti alloys with extremely low moduli.Finally, the properties of β-type Ti alloys, such as the mechanical properties, corrosion behavior, and even biocompatibility, are reviewed in comparison to other types of Ti alloys.

Design and Processing of Biomedical β-type Titanium Alloys
Similar to other hexagonal metals and alloys, Ti exhibits a hexagonal close-packed structure (HCP, α-Ti) at room temperature and transforms into a BCC β-Ti above the β transus temperature (883 • C for Ti) [22,[83][84][85][86][87].Therefore, to obtain β-type Ti alloys at room temperature, the addition of a relatively high fraction of β-stabilizers, such as Mo, Nb, Ta, Fe, and Cr, is required [46,88,89].Such β-stabilizing elements expand the β region and form infinite solid solutions with Ti above the β transus temperature in the binary phase diagrams [90,91].Therefore, generally, Ti alloys would consist of a metastable BCC β-phase after quenching from the temperature above β transus temperature if the addition of β-stabilizers exceeds a critical concentration.For example, a 10 wt.% addition of Mo in Ti-Mo binary alloys can form an infinite solid solution above 400 • C [91]; Ti-Nb binary alloys with 35 wt.% Nb would form an infinite solid solution above 425 • C [90].However, a metastable BCC β-phase would decompose into an HCP α ′ -martensite phase and/or the orthorhombic α ′′ -martensite in the condition of energy disturbance (including heat treatment and deformation) [72,74].In such a situation, it is possible to add enough β-stabilizers to lower the β transus temperature below room temperature in principle, thereby resulting in stable β-type Ti alloys.
Usually, the molybdenum equivalency (Mo eq ) method is used to predict the β phase stability of β-type Ti alloys, which is expressed as the following Equation (1): 5 + [Nb] where [x] indicates the content of the element [x] in wt.%.This equation is used to evaluate the equivalent effect of β-stabilizers in Ti alloys.Mo is selected as the baseline and normalizes other elements to an equivalent Mo value.Conversely, Al (α-stabilizer) plays a subtracted role in the Mo eq value.Other α-stabilizers, such as Zr, Sn, O, and N, can also be calculated as Al equivalency (Al eq ), according to the following equation: where [x] also indicates the content of the element [x] in wt.%.As such, total Mo eq can be calculated for a variety of Ti alloys.Minor variations may be reported for these two equations, because of the critical concentrations of elements between the American and Russian data [1].
A Mo eq value of approximately 10.0 is required to obtain 100% BCC β-phase after quenching from the β phase region [91].The β transus temperature is lowered as the value of Mo eq increases.The Mo eq values and β transus temperatures for some commercially β-Ti alloys and newly designed low-cost β-type Ti alloys as well as their elastic moduli are summarized in Table 1.As listed in Table 1, various Ti alloys are designed with different chemical compositions; a higher Mo eq generally results in more stable β-Ti alloys.The Mo eq method plays a significant role in designing new β-Ti alloys and has facilitated the development of a wide range of β-Ti alloys in the past decades, such as the Ti-Mo series [92,93], Ti-13Nb-13Zr [30,94], Ti-20Nb-10Zr-5Ta [95], Ti-11.5Mo-6Zr-4.5Sn[96,97], Ti-35Nb-5Ta-7Zr [51,98], and Ti-29Nb-13Ta-4.6Zr[99].Notably, Mo, Zr, Ta, and Nb metals have higher density than Ti.Therefore, alloying with such elements would increase the density of Ti alloys.As implants, the increase in weight may cause discomfort for the patients.As mentioned earlier, Mo, Zr, Ta, and Nb are also expensive, and the use of these elements would increase the cost of β-Ti alloys.Moreover, these alloying elements possess high melting points, inevitably causing difficulty in the alloy preparation.As such, new low-cost β-Ti alloys have been developed in recent years based on the molybdenum equivalency method, which primarily contains low-cost alloying elements, such as Fe, Mn, Sn, and Cr [71,72].Such newly designed low-cost β-Ti alloys also exhibit favorable properties for biomedical applications [100].Another important design method is the DV-Xα molecular orbital design method [108].In this method, two key parameters are used, namely, bond order (Bo) and metal d-orbital energy level (Md).Bo indicates the covalent bond strength between metal Ti and an alloying element, and Md represents the metal d-orbital energy level of transition metals as alloying elements, which is determined by the metallic radius of elements and the electronegativity.Correspondingly, Morinaga et al. established [109][110][111] the Bo−Md diagram to utilize the theoretical approach of the d electron theory; Bo and Md are average values for Bo and Md.This method not only indicates the phase stability and phase constituents of Ti alloy but also can predict their mechanical properties [112].The Bo−Md diagram has been reported in Ref. [101,108,111].Therefore, many β-type Ti alloys have been developed based on this DV-Xα molecular orbital design method.
According to the aforementioned methods, a variety of β-type Ti alloys were designed and produced in the past [96,113].Generally, β-type Ti alloys are produced by solidification/casting [93].Recently, Chirico et al. [114] reported a method to produce β-type Ti alloys using titanium hydride as feedstock by powder metallurgy.Such a method enhances the densification of Ti compacts, gets better control of contamination, and reduces the cost of raw materials.On the other hand, to obtain a required shape, the produced Ti bulks must undergo thermo-mechanical processing and/or heat treatment, which can also tailor the microstructures of β-type Ti alloys, especially for metastable β-type Ti alloys.As reported in the literature, general thermo-mechanical processing, including forging, rolling, and extrusion, was conducted on β-type Ti alloys to produce rods, sheets, and/or tubes, respectively [113].In the meantime, β-type Ti alloys are heat treatable and can be heated at solution-treated temperature followed by aging to enhance their strength [1].The phase transformation of β→α, β→α ′ and/or β→α ′′ takes place during aging in the solution-treated metastable β-type Ti alloys, hence causing dispersion strengthening [72].However, the strength of most β-type Ti alloys have satisfied strength to meet the requirement for use as implants.Therefore, extensive attention has been paid to decrease the elastic moduli of β-type Ti alloys to avoid the stress-shield effect.Although β-type Ti alloys have lower elastic moduli compared with other types of Ti alloys, the elastic moduli of β-type Ti alloys are still higher than those of the human bones.Therefore, porous β-type Ti alloys (other types of Ti and Ti alloys) [41, [115][116][117][118][119], in which their strength is sacrificed to obtain lower moduli, are produced by new preparation methods.

Some Preparation Methods for Porous β-type Ti Alloys
As seen in Figure 1, the elastic modulus of human bone is about 30 GPa, while the lowest elastic modulus of Ti-29Ni-13Ta-7.1Zralloy is 55 GPa.The mismatch of elastic modulus between the implant and adjacent bones would result in the stress-shielding effect [120].When the stress-shielding effect takes place, the bone would reduce the mass, namely, bone resorption [119,121,122].It has reported that the stress-shielding effect would lead to the thinning of the bone (external remodeling) or it becoming more porous (internal remodeling) [119,121,122].Meanwhile, the relative movement between the implant and the adjacent bone would take place owing to the modulus mismatch.Under the extreme situation, bone ingrowth would be inhibited so that implant osseointegration is unsuccessful [119].Fortunately, the development of porous materials could effectively lower the moduli of Ti and Ti alloys and therefore enable the possibility of the stress-shielding effect.The porous structure not only lowers the elastic moduli of Ti alloys but also enhances tissue adhesion and promotes the ingrowth of bone cells [116,123].Therefore, it is necessary to develop porous β-type Ti alloys for the actual applications.Up to now, there are a variety of preparation methods for porous materials, such as sintering, investment casting, and rapid prototyping [10,124].The various preparation methods would lead to the different properties of Ti and Ti alloys.Currently, two primary methods are frequently employed for preparing porous β-type Ti alloys, namely, powder metallurgy and additive manufacturing.

Powder Metallurgy
Powder metallurgy (PM) uses the powder of pure metals, blends, or alloys as raw materials, and it produces metallic parts by forming and/or sintering [125][126][127][128][129][130].Before the process of PM, the powder would be compressed in a mold, which aims to attain the required shapes and dimensions of the model [23,125,[131][132][133]. Afterward, the sintering process is conducted under a protective atmosphere in a high-temperature stove or a vacuum stove.PM allows the fabrication of amorphous materials, solid solutions as well as intermetallic phases from components with different melting points [131,[134][135][136].In addition, PM technology has high design freedom and could fabricate metallic parts with porous structures on a large scale [10].The porous metallic parts manufactured by PM may have different types of pores, such as through holes and blind holes [10].For porous implants, the size and morphology of pores should be controlled in the PM process, which has influences on bone ingrowth, osteointegration, and the fatigue resistance of the implants [137].PM has been employed to produce Ti and Ti alloys for many years [138].In recent years, porous Ti alloys are prepared by PM technologies for biomedical applications.Among various PM technologies, spark plasma sintering and the space holder method are commonly used for producing porous Ti and Ti alloys.
Spark plasma sintering (SPS) is a rapid sintering process, which employs the external current to assist powder consolidation [2,10].SPS directly exerts a pulse current between powder particles for Metals 2020, 10, 1139 6 of 29 heating and sintering the powder.Hence, sometimes, SPS is also called plasma-activated sintering, electrical field-activated sintering, or electrical discharge compaction [10].The SPS device includes a power supply (impulse current generator), pressure control, and vacuum chamber.Before sintering, metal powder is put into a mold and applied with pressing pressure as well as current.Subsequently, the powder used would experience discharge activation, thermoplastic deformation, and cooling.Finally, a high-performance part would be obtained.As such, SPS is a novel technology using electric energy combined with mechanical energy.SPS technology is frequently used in the biomedical field, which results in high biomechanical properties and the osteoconductivity of prepared porous materials [139].The advantages of low sintering temperature, low electric pressure, and short time make SPS become a priority for porous Ti and its alloys [2].Hussein et al. [140] successfully prepared nanostructured near-β Ti-20Nb-13Zr by SPS, and the results showed that a structure with nearly full density is obtained after SPS at 1200 • C. Sintering at the temperature below 1200 • C can obtain a porous structure (Figure 1a).The obtained alloy was chemically homogenized with a microhardness value ranging from 620 HV to 660 HV (Figure 1b).The developed Ti-20Nb-13Zr alloy prepared by SPS is proposed for dental and/or orthopedic applications.
β Ti------method is simple and easy to operate.For example, porous β -of 300-800 μm and micropores of several microns, is successfully fabricated by t the spacer was about 500-800 μm.Before sintering, the mixture is compressed to compact in a mold.sintering the compact (1200 °C for 10 h).According to this procedure, the porous β -spacer, the porosity of produced porous β --------- The space holder method is another PM technology, which is a modification of conventional powder metallurgy [141].The space holder method uses mixed metal powder and spacer particles as raw materials.The spacer particles act as pore formers to assure the homogeneity of the mixture [141,142].Then, the mixed powder is put into a mold and compressed together under a controlled pressure to form a solid part [10, [142][143][144].Afterward, either sintering or removal of the spacer (depending on the type of spacer) is used in the process, therefore leaving behind the new pores in the matrix [10,142].As such, the shape, size, and distribution of the pores, as well as the porosity, all depend on the selected spacer particles [10].Therefore, it is important to select an appropriate spacer material with low reactivity, which can be removed under relatively low temperatures [2,10].This method is simple and easy to operate.For example, porous β-type Ti-10Nb-10Zr, with macropores of 300-800 µm and micropores of several microns, is successfully fabricated by this method [145].The raw powder was primarily mixed with an ammonium hydrogen carbonate spacer.The size of the spacer was about 500-800 µm.Before sintering, the mixture is compressed to compact in a mold.Subsequently, the compact is sintered in two steps: (i) burning out the spacer (175 • C for 2 h) and (ii) sintering the compact (1200 • C for 10 h).According to this procedure, the porous β-type Ti-10Nb-10Zr with different porosity can be produced by adding different fractions of ammonium hydrogen carbonate spacer.By varying the fraction of the spacer, the porosity of produced porous β-type Ti-10Nb-10Zr can be controlled; therefore, the mechanical properties could be manipulated.Porous Ti-35Nb-5Ta-7Zr, Ti-10Mo, and porous Ti-24Nb-4Zr-8Sn (other types of Ti and Ti alloys as well) have also been successfully produced by this method [146,147].However, it also has some limits to produce porous materials.The accuracy of the pores is low, which may influence the structure of the produced porous material [2].

Additive Manufacturing
Additive manufacturing (AM), namely, 3D printing, is based on the discrete-collecting principle to achieve parts prototyping [148][149][150][151].In contrast to traditional subtractive manufacturing, AM techniques fabricate three-dimensional solid parts by a layer-by-layer method from bottom to top [148,[152][153][154].There is a range of advantages of AM techniques, including their short production cycle, simple machining process, fast commissioning, and high material utilization rate [155].More prominently, AM could prepare parts with complex geometry quickly and accurately, which is far more advantageous than the traditional subtractive manufacturing process [152,[155][156][157]. Through years of exploration and practice, AM could be used to produce metallic parts, such as Ti and Ti alloys, using laser or electron beam as heat sources from computer-aided designed (CAD) models [149,158].In recent years, AM-produced porous Ti alloys attracted a lot of attention; selective laser melting (SLM) and electron beam melting (EBM) stand in the breach in producing high-performance metallic parts [155,[159][160][161].
The SLM device mainly contains a controlling computer system, a laser emitter, a scanning system, and an automatic powder feeder [156].During the SLM process, metal powder is selectively heated up to complete melting by a computer-controlled laser beam and then quickly solidifies in a protective atmosphere [156].When the manufacturing of one layer is finished, the build platform would lower by the thickness of a layer.Subsequently, the powder feeding system sends newly applied powder from a moving container and deposits a new layer of powder on the previously formed solid layer [162].As such, this process is repeated until the entire CAD model is built.As such, SLM is a layer-wise process, which uses a scanning laser beam to selectively melt the metal powder to produce the metallic components with designed geometry (from a CAD model) [156].In general, the pre-set processing parameter set determines the properties of components.For instance, the relative density is closely related to the laser energy, which is defined as [163]: where P is the laser power (W), v is the scan speed (mm s −1 ), t is the layer thickness (mm), and s is scan spacing (mm).E is a function of these key parameters for the solidification and the quality of SLM-produced β-Ti components, thereby determining their performances.As shown in Figure 2a, Zhang et al. [25] used different laser scanning speeds to fabricate Ti-24Nb-4Zr-8Sn alloy and found that there is a gradual decrease in the density and hardness with increasing scanning speed (Figure 2a).A similar operation on laser energy density would also influence the properties of porous β-type Ti alloys [41,164].In addition to the processing parameters, the structure of porous β-type Ti alloy is also a main factor influencing their properties.Liu et al.
[159] investigated the manufacturing and mechanical behavior of 3 porous structures (cubic, topology optimized, and rhombic dodecahedron) for Ti-24Nb-4Zr-8Sn.As seen from the typical compressive stress-strain curves of these three structures (Figure 2b), the rhombic dodecahedron structure distinctly exhibits lower compressive strength.In the early development of SLM technology, only a few Ti alloys were produced due to the lack of pre-alloyed powder, especially the powder from β-type Ti alloys.Therefore, several β-type Ti alloys were produced by mixed powder.Zhao et al. [165] used a Ti-25Nb blend to produce the alloy and found some unmelted Nb particles in the microstructure.Vrancken et al. [166] used Ti-6Al-4V-ELI pre-alloyed powder mixed with 10 wt.% Mo powder to produce a novel metastable β titanium metallic composite and found residual Mo particles in the microstructure.Similar results are also observed for other selective laser melted β-type Ti alloys, such as Ti-35Nb [57], Ti-25Nb [165], Ti-26Nb [167,168], Ti-50Ta [169,170], Ti-37Nb-6Sn [171], Ti-20Zr-12Nb-2Sn [172], etc.The selective laser melted β-type Ti alloys always have heterogeneous microstructures, which has more or less of an influence on their properties.A simple example is the micro-galvanic effect that results from the different phases, which may degrade the corrosion resistance of produced Ti alloys.Therefore, in recent years, more types of pre-alloyed β-type Ti alloy powder have been developed.More β-type Ti alloys produced by selective laser melting were reported, including Ti-45Nb [173], Ti-35Zr-28Nb [174], Ti-15Mo-5Zr-3Al [68], Ti-13Nb-13Zr [175], etc.However, preparing pre-alloyed powder significantly increases the cost of SLM-produced β-type Ti alloys.Therefore, there is a long way to go for the commercial use of SLM-produced β-type Ti alloys.
Similar to SLM, the EBM process, as another AM technique, is capable of fabricating a series of engineering components directly from CAD models using an electron beam as the heat source [152,176,177].The EBM device generally contains a computer controlling system, a tungsten filament for emitting an electron beam, and a powder feeder system [152].The electron beam is launched by a tungsten filament when the filament is heated to a certain temperature.During the EBM process, a vacuum environment is used to protect the materials from oxidation.As such, EBM is capable of producing Ti parts with complex geometry directly.The properties of porous β-type Ti alloys are also influenced by the processing parameters of EBM.Liu et al. [42] prepared a porous β-type Ti-24Nb-4Zr-8Sn with 70% porosity using EBM and found that a lower scanning speed results in more input energy; thereby, the produced struts with higher yield strength and fewer flaws.Kurzynowski et al. [178] discussed the effect of the EBM process parameters on the porosity and microstructure of Ti-5Al-5Mo-5V-1Cr-1Fe alloy and pointed out that the maximum hardness is obtained at the energy input of 30 J/mm 3 and the scanning speed of 1800 mm/s.In addition, the Al content in Ti-5Al-5Mo-5V-1Cr-1Fe alloy is related to the scanning speed adopted.The lower the scanning speed (higher energy density), the higher the Al losses.Note that the produced parts of the EBM process have higher environmental (chamber) temperatures compared to the SLM process.The highest preheating temperature of SLM is only 300 • C, while that of EBM could be up to 600-1200 • C [2,42,152].Hence, the cooling rate in SLM is significantly higher than that in EBM.Such distinctions in the EBM and SLM processes can cause the fabricated parts of β-type Ti alloys produced by EBM and Metals 2020, 10, 1139 9 of 29 SLM to have different microstructures and therefore different mechanical properties.Taking β-type Ti-24Nb-4Zr-8Sn (Ti2448) alloy as an example to make a comparison between SLM and EBM, it can be found in Table 2 that the SLM-produced Ti2448 has a slightly higher compressive strength than its EBM-produced counterpart.However, the compressive strength and Young's moduli between SLMand EBM-produced Ti2448 are almost the same after annealing in the β phase region.These differences are attributed to the production of an α (or α ′ ) phase in Ti2448 during the AM fabrication.Nevertheless, the α (or α ′ ) phase could be dissolved after annealing over 750 • C [115].Besides the above most frequently used powder-bed methods, there are also other net-shape fabrication methods to produce porous β-type Ti alloys.For example, laser-engineered net shaping (LENS) involves a complete melting of metal/alloy powder using a high-power laser beam as the heating source to fabricate the net shape (or near-net shape) functional parts [181].In comparison to SLM and EBM, LENS belongs to the powder-feed method.In the LENS process, a molten metal pool on the substrate is created by a laser.Then, metal/alloy powder is injected into the pool, which melts and solidifies.According to the CAD models used for fabrication, porous structures can be produced.Porous CP-Ti and Ti-6Al-4V have been successfully fabricated by LENS, and their moduli can be tailored by controlling the porosity [119,182,183].It was reported that the moduli of produced materials can be tailored between 2 and 90 GPa, which well match those of the natural bones [181].However, due to the lack of β-type Ti alloy, there is rare research with respect to the production of porous β-type Ti alloy.So far, Kalita et al. [184] used the LENS technique to fabricate Ti-14Nb, Ti-17Nb, Ti-19Nb, Ti-23Nb, and Ti-31Nb bulk samples by mixed Ti and Nb powder.Therefore, it is believed that porous β-type Ti alloy may be fabricated by LENS in the near future.
Additionally, there are also some potential methods that can produce porous structures, such as blown powder directed energy deposition [185] and wire fed directed energy deposition [186].These two methods have successfully fabricated net-shaped Ti parts.Blown powder directed energy deposition has a better capability of producing thin-walled components featuring sharp corners [187] compared with wire fed directed energy deposition.By contrast, wire fed directed energy deposition has a higher deposition rate and lower cost compared to blown powder directed energy deposition [187].Boeing 787 structural components and external landing gear assembly with complex geometries have been fabricated by wire fed directed energy deposition using Ti-6Al-4V [187].There still exist rare reports regarding the production of porous β-type Ti alloys by these methods.However, due to the promising capabilities of blown powder directed energy deposition and wire fed directed energy deposition, β-type Ti alloys with complex geometry can also be produced if there is a corresponding feedstock.

FAST-Forge
Apart from additive manufacturing, FAST-forge technology proposed by Weston et al. [188] is another near-net shape fabrication method.This method uses shaped field-assisted sintering to consolidate Ti powder into a pre-forged billet at the first step and then is closed die hot forged to achieve a near-net shape part geometry.The forging step enhances the mechanical properties of the sintered Ti by refining the microstructure.It was reported that Ti-5Al-5V-5Mo-3Cr (Ti-5553, a high-strength β-type Ti alloy) has been successfully prepared by FAST-forge technology.The produced Ti-5553 exhibits a significantly lower grain size of 10 µm compared with its conventionally solution-treated counterpart (approximately 700 µm) [189].Therefore, The FAST-forge-produced Ti-5553 has a high hardness between 410 and 417 HV.However, in the authors' opinion, although FAST-forge technology can fabricate Ti parts with the expected geometry, a porous structure with high porosity is still difficult to achieve since the forging process is hardly conducted on the inner Ti part.

Mechanical Properties
A considerable number of β-type Ti alloys are currently applied as metallic biomaterials as implants, such as artificial hip joints, heart valves, dentistry, and so on [2,190,191].As such, orthopedic implants would bear the cyclic loading during body movement, which leads to micro-stress concentration by nicks or inhomogeneous microstructures [18].For a long lifetime of implants, high fatigue resistance and strength are required.In the past, Co-Cr-based alloys and α + β-type Ti alloys are the preferred alloys compared to other biomedical alloys [18].However, for now, β-type Ti alloys have become the first choice due to their achievable strength and good fatigue resistance [2,18,192].Kent et al. [193] studied the mechanical properties of Ti-24Nb-3Zr-2Sn-xMo alloys.They found that the cold-rolled Ti-24Nb-3Zr-2Sn-xMo alloys exhibit strength exceeding 900 MPa.Niinomi et al. [194] investigated the Ti-29Nb-13Ta-4.6Zralloy aging at 573 K and found that the fatigue strength of Ti-29Nb-13Ta-4.6Zr is enhanced while maintaining the modulus below 80 GPa after aging.Therefore, Ti-29Nb-13Ta-4.6Zrcould exhibit high fatigue resistance after a suitable thermo-mechanical treatment [18,194,195].Similarly, Laheurte et al. [196] also had the same conclusion on Ti-29Nb-11Ta-5Zr and Ti-29Nb-6Ta-5Zr.
In addition, an ideal implant material is expected to possess low elastic modulus, good plasticity, and wear resistance besides high fatigue resistance and strength [18,196].Apparently, β-type Ti alloys demonstrate closer moduli to the human bone in comparison to α-type Ti alloys and α + β-type Ti alloys.Even if other soft tissues have lower elastic moduli than cortical bones, novel porous structure β-type Ti alloys could satisfy these requirements (Table 2).To obtain the desired mechanical properties of β-type Ti alloys, alloying elements are significantly important.Ehtemam-Haghighi et al. [76] found that the addition of Fe would reduce the formation of α" martensite and hence improve the stability of the β phase in Ti-11Nb-xFe alloys.With the increasing content of Fe, the strength of Ti-11Nb-xFe also increases.Using such elements to design new β-type Ti alloys with controllable mechanical properties is an available and economic process.Likewise, Jawed et al. [104] found that the addition of Zr and Mn in Ti-Nb alloys would result in different microstructures (Figure 3).Apparently, the microstructures of β-type Ti-Nb-Zr-Mn alloys changes with altering the Zr and Mn contents.The equiaxed β grains are observed in all Ti-Nb-Zr-Mn alloys.It is noted that the addition of Mn reduces the average grain size of Ti-Nb-Zr-Mn alloys.Mn is a high growth-restriction factor when applied to Ti and Ti alloys.During solidification, the addition of Mn results in the rapid buildup of constitutional undercooling, and therefore, nucleation can take place before an advancing solid-liquid interface.Hence, the grains are refined [197].In comparison, the average grain size of Ti-Nb-Zr-Mn alloys increases with increasing the Zr content.The addition of Zr has both the solution strengthening and fine-grain strengthening effect.Zr also acts as β-stabilizer.When the addition of Zr exceeds a certain content, the stability of the β-phase enhances remarkably, which significantly lowers the (α + β)/β phase transformation temperature.As such, the superheat increases markedly and the β grains coarsen [198].Therefore, the microstructures of Ti-Nb alloys can be tailored.Xu et al. [199] developed a new β-type Ti-5Mo-Fe-3Sn that shows a low elastic modulus of 52 GPa and high yield strength of 740 MPa.The reason for these desired properties is attributed to the combined addition of Sn and Fe suppressing the formation of the ω phase and introducing solid solution strengthening.Hence, selecting the appropriate elements to add to β-type Ti alloys is beneficial to controlling their mechanical properties.(Reproduced with permission from ref. [104].Copyright (2020), Elsevier).
On the other hand, heat treatment and thermo-mechanical processing also can manipulate the microstructures of β-type Ti alloys and tailor their mechanical properties.Liang et al. [200] developed a new β-type Ti alloy of Ti-31Nb-6Zr-5Mo by the d-electron method using a vacuum nonconsumable furnace.Solution treatment with and without aging treatment were conducted after hot rolling of this alloy.The Nb-rich fibrous grains produced by hot rolling are re-dissolved during solution treatment at 800 • C for 30 min.The alloying elements in Ti-31Nb-6Zr-5Mo become homogeneous after solution treatment.After aging treatment at 300 • C for 2 h, the Nb element redistributes to form the Nb-rich and Nb-depleted β regions.Both solution-treated and aging-treated samples show the identical crystallographic structure of the monolithic β phase.However, different moduli of 44 GPa and 48 GPa are observed for solution-treated and aging-treated samples, respectively.This finding indicates that heat treatment can influence the distribution of alloying elements and therefore the mechanical properties.Coakley et al. [201] found that the cold-rolled Ti-24Nb-4Zr-8Sn exhibits a martensitic α ′′ -precipitate/β-matrix microstructure.After aging treatment at 300 • C for 4 h and 8 h, the number density of Nb domains (which are associated with superelasticity) decreases, which deteriorates their mechanical properties (Figure 4).Kuroda et al. [202] exerted homogenization, hot rolling, and annealing on a Ti-20Zr-xMo ternary alloy system (Mo = 0, 2.5, 5, 7.5 and 10 wt.%) and found that the volume fraction of the β phase increases with the increasing Mo content.For homogenized samples, their moduli ranges within 93-105 GPa, regardless of the Mo content.Similar results are also found in the annealed samples [202].However, for hot-rolled samples, the modulus of the sample decreases with the increasing Mo content.The modulus of Ti-20Zr is 106 ± 4 GPa, which is significantly higher than that of Ti-20Zr-10Mo (79 ± 4 GPa).This is because hot rolling induces the alteration of the phase constituent of Ti-20Zr-xMo, and the Mo addition increases the stability of the β phase in the microstructure.It can be found that the number density of Nb domains decreases with the increasing aging time.
Other microstructural characteristics can also influence the mechanical properties of β-type Ti alloys.Gao et al. [172] pointed out that reducing the grain size of Ti-20Zr-12Nb-2Sn (at.%) would obtain a higher recovery strain, which is an interesting phenomenon.Since the elastic modulus is known to be dependent on the crystallographic orientation of the Ti alloys, controlling their texture can tailor their moduli in theory.For Ti-15Mo-5Zr-3Al alloy, the highest value of the modulus is perpendicular with (111) and the lowest value of the modulus is perpendicular with (001) [203].Ishimoto et al. [68] used different scan strategies in selective laser melting to control the texture of a Ti-15Mo-5Zr-3Al alloy and successfully obtained a primary (001) texture along with the building direction by a bidirectional scanning strategy with a rotation of 90 • between layers (Figure 5).Therefore, a low modulus of Ti-15Mo-5Zr-3Al alloy along with the building direction is achieved.This is because the different scan strategies change the direction of the maximum thermal gradient.Similar work was conducted by Pellizzari et al. [204] using such a method, and they obtained a metastable Ti-15Mo-3Al-3Nb alloy with a low modulus of 53 GPa.Ti-13Nb-13Zr is an early developed metastable β-type Ti alloy with low cost.However, it was reported that the Ti-13Nb-13Zr alloy has a modulus with a lowest boundary of approximately 65 GPa [205].Lee et al. [205] used cold caliber rolling to process Ti-13Nb-13Zr and obtained a <0002> orientation along with the normal direction.Therefore, a lower modulus of 47 GPa is achieved.
-Meanwhile, good wear resistance should be considered for β 3 summarizes the mechanical properties of different β β α + β similar in yield strength, while β type Ti alloys could have higher yield strength than α ---higher than that of α alloys.However, the elastic moduli of β whole, the mechanical properties of β Meanwhile, good wear resistance should be considered for β-type Ti alloys also.Yang et al. [67] investigated the corrosion-wear properties of Ti-12Mo-6Zr-2Fe and Ti-6Al-4V in simulated body fluid and found that Ti-12Mo-6Zr-2Fe and Ti-6Al-4V have comparable corrosion-wear resistance, although Ti-12Mo-6Zr-2Fe has a lower hardness.Therefore, Ti-12Mo-6Zr-2Fe can be a candidate for biomedical materials.Table 3 summarizes the mechanical properties of different β-type Ti alloys.Some of the β-type Ti alloys have comparable hardness with α + β-type alloys.The situation is similar in yield strength, while β-type Ti alloys could have higher yield strength than α-type alloys.The fracture strains of Ti-11Nb-7Fe and Ti-35Nb are significantly higher than that of α-type Ti alloys.However, the elastic moduli of β-type Ti alloys are significantly lower.Therefore, as the whole, the mechanical properties of β-type Ti alloys are desired.

Corrosion Behavior
It is well known that Ti and its alloys demonstrate good corrosion resistance in the various environments due to the formation of a stable passive film (mainly consisting of TiO 2 ) [2,158,[208][209][210].Even if the passive film on Ti samples is broken, the passive film can be re-built in a very short time.In the early stage, α-type and α + β-type Ti alloys are commonly applied for biomedical applications.Generally, the corrosion behavior of metallic materials depends on several factors: applied environment, alloy compositions, and microstructure [127,[211][212][213][214]. The human body has a relatively stable environment, while human temperature, environmental chemistry, and pH would change in some cases (e.g., inflammation and allergy).Alves et al. [215] investigated the corrosion resistance of CP-Ti and Ti-6Al-4V in simulated body fluid at 25 • C and 37 • C, respectively and found that the corrosion resistance of CP-Ti and Ti-6Al-4V is better at 25 • C. Therefore, the temperature has a significant influence on the corrosion behavior of CP-Ti and Ti-6Al-4V.Similarly, the pH value also influences the corrosion behavior of Ti-6Al-4V [216].In the neutral Ringer's solution, Ti-6Al-4V has good corrosion resistance, while its passive range is reduced at pH = 8 [216].According to the literature [217], Ti-6Al-4V exhibits duct-shaped pits along the grain boundaries in the simulated body fluid, which is considered to be related to the dissolution of V-rich zones.As such, the pitting corrosion of Ti-6Al-4V often takes place in the oral environment, which is attributed to the greater availability of oxygen and acidic foods [3].Kumar et al. [80] found that Ti-15Mo, CP-Ti, and Ti-6Al-4V alloys all have good corrosion resistance in Ringer's solution, while only Ti-15Mo shows a stable passive film in the fluoride solution.The high fluoride solution is inevitable in the human body environment, such as dental cleaning [209,217].Therefore, α-type and α + β-type Ti alloys show inferior corrosion resistance compared with β-type Ti alloys in such environments.Furthermore, for bearing metallic orthopedic implants, fretting corrosion should be considered [217].Fretting corrosion is usually presented at modular junctions and decreases via the formation of a protective oxide layer [217].Hence, it is highly essential to select appropriate Ti alloys with high corrosion resistance for biomedical applications.
Thanks to the development of β-type Ti alloys, they become candidates for biomedical applications.It is reported that β-type Ti alloys have good performance in a variety of corrosive environments.Wang et al. [57] found that an SLM-produced Ti-35Nb alloy could quickly form a stable passive film (mainly consisting of TiO 2 and Nb 2 O 5 ) to protect itself.The stable passive film covers the entire metal surface and effectively reduces the corrosion rate.However, the quality of the passive film is significantly influenced by the chemical homogeneity of the underlying substrate.Generally, SLM-produced Ti-35Nb using mixed powder always results in a heterogeneous microstructure with individual Nb grains.Wang et al. [57] found that the heat treatment of SLM-produced Ti-35Nb at 1000 • C for 24 h in an Ar atmosphere significantly promotes the chemical homogeneity of the Ti-35Nb substrate.Therefore, the heat-treated Ti-35Nb has a higher corrosion potential of −0.46 V versus saturated calomel electrode (SCE) than the SLM-produced Ti-35Nb (−0.55 V versus SCE).Alves et al. [211] also demonstrated that the corrosion resistance of β-type Ti alloys depends on the stability of passive films.They found that Ti-10Mo alloy shows significantly low passive current densities, especially after heat treatment.Certainly, there are many comparative investigations with respect to the corrosion behavior of three types of Ti alloys, which aim to develop more appropriate Ti alloys for biomedical applications.Bai et al. [43] compared the corrosion behavior among CP-Ti, Ti-6Al-4V, and Ti-24Nb-4Zr-8Sn in the simulated physiological environment.Their results showed that the Ti-24Nb-4Zr-8Sn alloy has a wider passive region as compared to CP-Ti and Ti-6Al-4V.Moreover, the Ti-24Nb-4Zr-8Sn alloy has a relatively low corrosion current density, which is comparable to CP-Ti and Ti-6Al-4V, attributing to the formation of the stable passive film primarily consisting of titanium and niobium oxides on its surface.Kumar et al. [80] also studied the corrosion behavior of CP-Ti, Ti-6Al-4V, and Ti-15Mo in the Ringer's solution, and they found that the passivation range of Ti-15Mo alloy (166-2513 mV versus SCE) is greater than those of CP-Ti (145-1522 mV versus SCE) and Ti-6Al-4V (155-1460 mV versus SCE).Chui et al. [218] investigated the corrosion behavior of the as-cast Ti-Zr-Nb-Mo alloys with different Mo contents.The results showed that the grain size of the Ti-Zr-Nb-Mo alloy decreases with increasing Mo content due to the presence of Mo causing constitutional undercooling, and the Ti-Zr-Nb-Mo alloy with a 15 wt.% addition of Mo shows the lowest passivation current density of 2.31 ± 0.03 µA cm −2 .Zareidoost et al. [219] separately added Fe, Sn, and Ag to Ti-25Zr-10Nb-10Ta and found that the alloy with Ag addition shows the best corrosion resistance in the Ringer's solution.The standard electrode potential of Ag (0.799 V) is more positive than that of Ti (−0.98 V), leading to the increase in the stability of passive film formed on Ti-25Zr-10Nb-10Ta.Therefore, Ti-25Zr-10Nb-10Ta-1.5Ag shows better corrosion resistance in Ringer's solution.Lin et al. [220] controlled the microstructure of Ti-40Ta-22Hf-11.7Zr by different solution treatment and aging treatment schemes.The results showed that the as-cast Ti-40Ta-22Hf-11.7Zrshows a β + ω microstructure, which transforms to monolithic β phase after being solution-treated at 900 • C for 1 h.After aging at 300 • C for 15 min, 1.5 h, 12 h, and 24 h, the β-phase gradually transforms into β + α ′′ , β + α ′′ + α, and β + α + ω.Such different microstructures of Ti-40Ta-22Hf-11.7Zralloys cause their distinct electrochemical behavior in Hank's solution.The solution-treated sample with a single β microstructure shows the lowest current density of 0.49 ± 0.03 µA cm −2 .
In several previous studies, the SLM-produced Ti-6Al-4V alloys would be prone to pitting corrosion in 3.5 wt.% NaCl solution compared with the counterparts produced by traditional methods, while EBM-produced Ti-6Al-4V alloy has better corrosion resistance than the wrought counterpart in phosphate-buffered saline [158,221].Therefore, an open question is asked: Is there a distinct corrosion behavior of Ti alloys produced by different preparation methods?To answer this question, Qin et al. [157] compared the corrosion behavior of SLM-produced and traditional monolithic Ti-24Nb-4Zr-8Sn alloys.These two alloys have the same chemical composition and monolithic β phase but different microstructures.As seen from Figure 6 [157], the potentiodynamic polarization curves and Nyquist plots of both alloys are nearly overlapping.Therefore, it can be understood that the distinctions in the corrosion behavior of Ti-6Al-4V alloys produced by different methods are related to the formation of different phase constituents in the microstructure.In comparison, monolithic β-phase Ti-24Nb-4Zr-8Sn alloys produced by various methods show similar corrosion behavior.Meanwhile, due to their monolithic phase in the microstructure, many β-type Ti alloys also possess high pitting corrosion resistance.However, for some metastable β-type Ti alloys, thermo-mechanical processing and heat treatment may trigger the phase transformation of β→α, β→α ′ , and/or β→α ′′ .Therefore, different phases in the microstructure of Ti alloys would produce the micro-galvanic effect during corrosion [222].Table 4 lists the corrosion potentials, corrosion current densities, and high-potential passive current densities of Ti-6Al-4V ELI, Ti-35Nb-7Zr-5Ta, Ti-13Mo-7Zr-3Fe (as-received α + β), and Ti-13Mo-7Zr-3Fe (metastable β) alloys in Ringer's solution at 37 • C after 1-h immersion [222].Both Ti-13Mo-7Zr-3Fe (as-received α + β) and Ti-13Mo-7Zr-3Fe (metastable β) alloys show better corrosion resistance than Ti-6Al-4V, and monolithic-phase Ti-13Mo-7Zr-3Fe (metastable β) exhibits better corrosion resistance than Ti-13Mo-7Zr-3Fe (as-received α + β).Therefore, it can be understood that the corrosion behavior of Ti alloys is mainly influenced by their phase constituents.Table 4. Corrosion potentials, corrosion current densities, and high-potential passive current densities of the Ti-6Al-4V ELI, Ti-35Nb-7Zr-5Ta, Ti-13Mo-7Zr-3Fe (as-received α + β), and Ti-13Mo-7Zr-3Fe (metastable β) alloys in Ringer's solution at 37 • C after 1-h immersion [222].Generally, Cl − is presented in a variety of environments, such as the human body, marine, coast environment, and chemical environment [223][224][225].Cl − ions are aggressive ions in the corrosive environments, which can damage the passive film formed on many metallic components [226][227][228].Therefore, the investigation on the corrosion behavior of Ti alloys in the Cl -environment can estimate their corrosion rates.Schutz [229] summarized the corrosion rate of various Ti alloys in boiling HCI solution at different concentrations and pointed out that most β-type Ti alloys show better corrosion resistance than Ti-6Al-4V.This finding illustrates that the passive films formed on β-type Ti alloys are more stable than that formed on Ti-6Al-4V.The better corrosion resistance enables β-type Ti alloys to be good potential biomedical materials.

Biocompatibility
Apart from the mechanical and corrosion properties, excellent biocompatibility is required for implant materials.Ideal materials can be implanted in the human body for a long period without a second surgery.After implantation, the materials would induce a considerable number of reactions in the human body with body fluid, proteins, and cells.Conventional α + β-type Ti alloys always contain detrimental elements.Therefore, β-type Ti alloys have been developed in recent years, and the corresponding investigation on the biocompatibility of β-type Ti alloys was also conducted.McMahon et al. [230] compared the cytocompatibility between Ti-26Nb and Ni-49.2Ti, and they found that Ti-26Nb is less cytotoxic.Xue et al. [231] pointed out that the Ti-19Zr-10Nb-1Fe alloy has similar cytocompatibility with the Ni-Ti alloy but better hemocompatibility.The improved biocompatibility of β-type Ti alloys can be attributed to the absence of toxic alloying elements.Up to date, the investigation on the biocompatibility of β-type Ti alloys is still at a very early stage.Further investigation regarding β-type Ti alloys is imminently required.
On the other hand, due to the biological inertia of Ti alloys, fibrous tissue capsules are prone to form on the implant surface [2].Such a phenomenon is inevitable for all types of Ti alloys.The biological inertness leads the β-type Ti alloys to be safe but not bioactive.Therefore, although β-type Ti alloys are free of toxic alloying elements, further improving the capability of osseointegration should be considered.Generally, surface modification with the aim to improve the bioactivity of Ti alloys has received a considerable amount of attention.For such a purpose, Takematsu et al. [232] alkali solution treatments on Ti-29Nb-13Ta-4.6Zrby electrochemical, hydrothermal, or mixed processes for different times, and the results showed that regardless of the methods or parameters used, the surface of Ti-29Nb-13Ta-4.6Zrbecomes mesh-like and has a strong ability to induce the formation of apatite.Dikici et al. [233] synthesized calcium phosphate/TiO 2 composite coatings on Ti-29Nb-13Ta-4.6Zrby the sol-gel method; they found that the coating can significantly enhance its bioactivity, since both calcium phosphate and TiO 2 are highly bioactive to bone cells.Besides inorganic coatings, organic coatings (or layers) have also received extensive attention.In the last few decades, the immobilization of extracellular matrix (ECM) proteins on the surface of Ti implants has been developed, which has been conducted on CP-Ti and Ti-6Al-4V [234].For instance, CP-Ti coated with collagen has a higher bioactivity for human mesenchymal cells [234].Similar results are also found in other coatings [235].Unfortunately, there is still rare literature about the organic coatings on β-type Ti alloys.However, due to the large success of organic coatings on other types of Ti alloys, β-type Ti alloys with bioactive coatings are expected to be a future trend for biomedical Ti alloys.

Conclusions
Good mechanical properties, excellent corrosion resistance, and admirable biocompatibility are the basic requirements for biomedical materials.Therefore, β-type Ti alloys are the preferred choice.As such, β-type Ti alloys have received a considerable amount of attention in the past few decades.For better development and application in the future, many studies have been conducted to investigate the β-type Ti alloys from alloy design and manufacture to properties.Therefore, this review introduces the biomedical β-type Ti alloys in terms of development, design, new preparation methods, and various properties.Biomedical β-type Ti alloys are developed later than α-type and α + β-type Ti alloys in the requirements of low elastic modulus and non-toxic alloying elements.Designing a β-type Ti alloy requires the addition of a certain fraction of β-stabilizers.The molybdenum equivalency (Mo eq ) method is frequently used to predict the β-phase stability of β-type Ti alloy, which is also considered as a significant convenience for designing new β-type Ti alloys.Although β-type Ti alloys have lower elastic moduli than other types of Ti alloys, the elastic moduli of β-type Ti alloys are still higher than those of human bones.Therefore, porous β-type Ti alloys with lower elastic modulus as well as higher tissue adhesion are developed.Additive manufacture (such as selective laser melting and electron beam melting) and powder metallurgy (such as spark plasma sintering and the spacer hold method) are commonly used to produce porous β-type Ti alloys.Afterwards, the properties of β-type Ti alloys are reviewed in view of their mechanical properties, corrosion behavior, and biocompatibility.Fortunately, β-type Ti alloys could perform well in these three aspects.Although β-type Ti alloys have been used as biomedical materials, further investigations are still recommended to increase their reliability and bioactivity in the human body in long-term service.Therefore, in the authors' opinion, porous β-Ti alloys with bioactive coatings may be the future trend for biomedical implants.

Figure 5 .
Figure 5. (a,c) Inverse pole figure (IPF) images from the three orthogonal planes.(b,d) (001), and (011) pole figures of the Ti parts measured in the y-z plane.BD is the building direction and SD is the scanning direction.(Reproduced with permission from ref. [68].Copyright (2017), Elsevier).
t Ultimate tensile strength; c Ultimate compressive strength.

Table 3 .
Mechanical properties including hardness (H), yield strength (σ 0.2 ), ultimate strength (σ max ), fracture strain (ξ max ), and elastic modulus (E) for different types of Ti alloys by a variety of fabrication methods.
t Ultimate tensile strength; c Ultimate compressive strength.