Dynamic Behavior of a Novel High-Strength and Ductile Near-α Titanium Ti-Al-Mo-Zr-Fe-B Alloy

: In this study, the dynamic compression properties of a new high-strength (>1000 MPa) and ductile (>15%) near-α titanium Ti-6Al-1Mo-2Zr-0.55Fe-0.1B alloy were investigated at high strain rates of 1620 s − 1 ~2820 s − 1 by a split Hopkinson pressure bar (SHPB). The microstructural evolution of the samples before and after the dynamic deformation was analyzed by electron backscatter diffraction (EBSD). The results indicated that the strength of the alloy enhanced signiﬁcantly under the dynamic loading compared with the quasi-static compression and increased with the increase in the strain rate. An abundance of deformation twins released the dislocation pile-up and coordinated the plastic deformation of alloy during the dynamic loading. The dynamic plasticity constitutive equation of the alloy was obtained by ﬁtting high strain rate experimental data at room temperature by the Johnson–Cook constitutive equation with the modiﬁed temperature term.


Introduction
Near-α titanium alloys have high specific strength, excellent corrosion resistance, and good weldability, making them extensively accepted as admirable structural materials in marine engineering [1][2][3][4][5].In particular, the Ti80 (Ti-6Al-3Nb-2Zr-1Mo) alloy is widely studied and applied as a typical marine titanium alloy because of its corrosion resistance [6,7], impact toughness [8], low fatigue cracking [9,10], and creep behavior [11] as well as its performance after various welding methods [12,13].However, the presence of the Nb element makes Ti80 expensive; it also gives it a high melting point of up to 2468 • C. The high melting point makes it possible to generate a high density of inclusions in the casting process, which is harmful to the subsequent forging/rolling process.Moreover, the strength of the Ti80 is approximately equal to 800 MPa, which is not high enough as the pressure shell of the deep-diving submersible dives into the depth of up to 10,000 m.That is why the new type, the 10,000 deep-diving submersible, used α + β alloy in spite of poor weldability.
On the other hand, titanium alloys as structural materials are often subjected to high velocity impact loads, which are required to ensure the structural integrity and continuity with the required dynamic load carrying capacity under the specified impact loads.Since both plasticity and failure behavior of titanium are significantly affected by the strain rate, it is necessary to study the dynamic behavior of titanium at different strain rates [14][15][16].Hence, in this work, a novel near-α titanium Ti-6Al-1Mo-2Zr-0.55Fe-0.1Balloy, based on the Ti80 alloy, was designed, in which Nb was replaced by the microalloying elements Fe and B. The aim of the present investigations was to design a novel, low-cost, high-strength, and high-toughness near-α titanium alloy for marine engineering applications and evaluate the dynamic compression properties of this alloy at different strain rates with the split Hopkinson pressure bar (SHPB).

Materials and Methods
A near-α titanium Ti-6Al-1Mo-2Zr-0.55Fe-0.1Balloy was designed and melted using vacuum arc fusion (VAR) equipment.The chemical composition of the alloy was investigated by inductively coupled plasma mass spectrometry (ICP-MS) analysis; the actual chemical composition is shown in Table 1.The phase transition temperature of the alloy measured by the metallographic method was 995 • C.After forging, heat treatment [17] was used to optimize the microstructure.
Table 1.Chemical composition of the near-α Ti-6Al-1Mo-2Zr-0.55Fe-0.1B(wt.%) alloy.Quasi-static tensile tests were conducted on the MTS 370.10 hydraulic servo fatigue tester.The tensile specimen length was 100 mm, and the diameter and length of the gauge were φ5 mm and 25 mm, respectively.The strain rate was 7 × 10 −3 s −1 .Quasi-static compression experiments were carried out on a universal testing machine with a strain rate of 10 −3 s −1 with the dimension of φ3 × 6 mm, which was the sample size.Dynamic mechanical properties were tested by the SHPB equipment at high strain rates of 1620 s −1 ~2820 s −1 , and the sample size was φ6 × 3 mm.The diameter of the SHPB compression bar was 14.5 mm, and the input pulse maximum value was 1200 MPa.The samples were prepared by wire cutting, and the end faces were polished by sandpaper grinding.

Elements
The Japanese Regulus 8100 cold field emission scanning electron microscope was used to characterize the microstructure of the samples as well as the element distribution; the sample size was 4 mm × 4 mm.After dynamic deformation, EBSD samples were prepared by slicing parallel to the compression direction, and the samples were polished using a Shanghai metallographic PFD-2 electrolytic polishing machine with an electrolytic solution of 12 mL perchloric acid, 120 mL methanol, and 68 mL n-butanol.The polishing temperature was stabilized at −20 • C by adding liquid nitrogen; the polishing current was 0.6~0.7 A, and the polishing time was about 50 s.The surface of the specimen was cleaned with alcohol after polishing.The EBSD was carried out on the field emission scanning electron microscope (SEM, JSM-6700F), equipped with an Oxford Instruments EBSD detector and working at an accelerating voltage of 20 KV.The step size of the samples was 0.05 µm with a scanning area of 1600 µm 2 .The HKL Technology Channel 5 system was used to analyze the EBSD test data.

Initial Microstructure
The SEM microstructure and composition distribution map of the Ti-6Al-1Mo-2Zr-0.55Fe-0.1Balloy is illustrated in Figure 1.Obviously, the bimodal microstructure with the primary equiaxed α phase and β transformation matrix was achieved by the heat treatment, which was accepted as a result of the simultaneous combination of good strength and ductility [18,19].The size of the primary equiaxed α phase was about 5.25 µm, occupying 21% of the content.The thickness of the secondary lamellar α phase was about 0.52 µm.On the other side, the distribution of each alloying element showed sufficient homogeneity, as indicated in Figure 1b.

Quasi-Static Tensile and Compression Experiment
Figure 2a shows the true stress−strain curve for the alloy at the strain rate of 0.007 s −1 .Result indicated that the yield stress was 927 MPa; the stress increased slightly with the increase in the strain, and the ultimate tensile stress could reach 1005 MPa.In comparison with a slight increase in the work hardening effect during the tensile test, the alloy showed a significantly higher work hardening during the quasi-static compression experiment (Figure 2b).Simultaneously, the ultimate compression stress increased up to 1370 MPa from 1081 MPa of tensile yield stress.Table 2 shows the quasi-static mechanical property data of the new titanium alloy and the Ti80 alloy with the bimodal microstructure.It can be seen that the strength of the novel alloy is superior to that of the Ti80 alloy.Meanwhile, good ductility is kept at the same level.

Quasi-Static Tensile and Compression Experiment
Figure 2a shows the true stress−strain curve for the alloy at the strain rate of 0.007 s −1 .Result indicated that the yield stress was 927 MPa; the stress increased slightly with the increase in the strain, and the ultimate tensile stress could reach 1005 MPa.In comparison with a slight increase in the work hardening effect during the tensile test, the alloy showed a significantly higher work hardening during the quasi-static compression experiment (Figure 2b).Simultaneously, the ultimate compression stress increased up to 1370 MPa from 1081 MPa of tensile yield stress.Table 2 shows the quasi-static mechanical property data of the new titanium alloy and the Ti80 alloy with the bimodal microstructure.It can be seen that the strength of the novel alloy is superior to that of the Ti80 alloy.Meanwhile, good ductility is kept at the same level.

Quasi-Static Tensile and Compression Experiment
Figure 2a shows the true stress−strain curve for the alloy at the strain rate of 0.007 s Result indicated that the yield stress was 927 MPa; the stress increased slightly with t increase in the strain, and the ultimate tensile stress could reach 1005 MPa.In comparis with a slight increase in the work hardening effect during the tensile test, the alloy show a significantly higher work hardening during the quasi-static compression experime (Figure 2b).Simultaneously, the ultimate compression stress increased up to 1370 M from 1081 MPa of tensile yield stress.Table 2 shows the quasi-static mechanical proper data of the new titanium alloy and the Ti80 alloy with the bimodal microstructure.It c be seen that the strength of the novel alloy is superior to that of the Ti80 alloy.Meanwhi good ductility is kept at the same level.

Dynamic Compression Experiment
Dynamic true stress−strain curves of the Ti-6Al-1Mo-2Zr-0.55Fe-0.1Balloy at different strain rates are shown in Figure 3a.Obviously, compared to the quasi-static stress−strain curve (Figure 2b), they had no obvious yield stage and strain hardening during dynamic loading.The strength was higher during the high strain rate deformation and increased with the increase in the strain rate.Meanwhile, all the dynamic stress−strain curves fluctuated at the plastic deformation stage.The main data extracted from the dynamic stress−strain curves of the novel alloy and the Ti80 alloy are listed in Table 3.Among them, the absorbed impact energy could be considered as the area under the stress−strain curve of the uniform plastic deformation, which could reflect the dynamic mechanical property of materials more accurately by considering the combination of the strength and plasticity.The formula for calculating the absorbed impact energy is as follows [22]: where ε f and ε s are strains at the beginning and the end of the plastic deformation, respectively.It can be seen that the absorbed impact energy of the novel alloy increases with an increase in the strain rate, exhibiting a higher value than the Ti80 alloy at the similar strain rate.
tals 2022, 12, x FOR PEER REVIEW 4 of and increased with the increase in the strain rate.Meanwhile, all the dynamic stress−str curves fluctuated at the plastic deformation stage.The main data extracted from the d namic stress−strain curves of the novel alloy and the Ti80 alloy are listed in Table Among them, the absorbed impact energy could be considered as the area under stress−strain curve of the uniform plastic deformation, which could reflect the dynam mechanical property of materials more accurately by considering the combination of strength and plasticity.The formula for calculating the absorbed impact energy is as f lows [22]: where and are strains at the beginning and the end of the plastic deformation, spectively.It can be seen that the absorbed impact energy of the novel alloy increases w an increase in the strain rate, exhibiting a higher value than the Ti80 alloy at the simi strain rate.

Alloy Composition
Ti-6Al-1Mo-2Zr-0.55Fe-0.1BThe strain hardening rate θ can be used to express the ability of a material to res plastic deformation, where θ  dσ/d.Figure 3b shows the strain hardening rate of sa ples at the high strain rates of 1620 s −1 and 2820 s −1 .The strain hardening rate curves d veloped similarly at the beginning of the deformation, and the alloy underwent contin ous plastic deformation, which led to the first peak stress at the strain 0.04.After that, development of the strain hardening rate was non-monotonous.This implies that the th mal softening effect happened during the dynamic loading.It is well known that adiaba heating is always generated as a result of accumulated plastic work during the dynam loading when the generated heat cannot dissipate outside in a short time, which increa  The strain hardening rate θ can be used to express the ability of a material to resist plastic deformation, where θ = dσ/dε.Figure 3b shows the strain hardening rate of samples at the high strain rates of 1620 s −1 and 2820 s −1 .The strain hardening rate curves developed similarly at the beginning of the deformation, and the alloy underwent continuous plastic deformation, which led to the first peak stress at the strain 0.04.After that, the development of the strain hardening rate was non-monotonous.This implies that the thermal softening effect happened during the dynamic loading.It is well known that adiabatic heating is always generated as a result of accumulated plastic work during the dynamic loading when the generated heat cannot dissipate outside in a short time, which increases the local temperature in materials and leads to the dislocation annihilation.The wave-shape curves indicate the competition of strain hardening and thermal softening of the alloy during dynamic loading [23].When the strain hardening rate θ > 0, the strain hardening effect dominates in the plastic deformation of the alloy, and when θ < 0, it shifts to be dominated by the thermal softening effect.Obviously, for the investigated deformation with two strain rates, the final hardening rate was negative at the strains of 0.19 and 0.3, which shows the advantage of the thermal softening effect.
The inverse pole figures for the initial and dynamically deformed samples are shown in Figure 4a-c.The results indicated that the initial microstructure was homogeneous as a result of heat treatment, and the grain size was about 6.43 µm.After the dynamic compression, the grains suffered fragmentation, and the grain size decreased up to 5.51 µm and 5.3 µm after high strain rates of 1620 s −1 and 2820 s −1 , respectively.On the other hand, deformation twins activated in the microstructure as a result of dynamic loading and promoted the increase in the strain rate.The morphology of the deformation twins showed diversity under dynamic loading, including twin boundaries terminated at the grain boundaries, those terminated within the grains, and even the generated penetrating twins.Meanwhile, a twin wafer-like microstructure was found in the sample subjected by dynamic loading at 2820 s −1 .stals 2022, 12, x FOR PEER REVIEW 5 o with two strain rates, the final hardening rate was negative at the strains of 0.19 and 0 which shows the advantage of the thermal softening effect.The inverse pole figures for the initial and dynamically deformed samples are sho in Figure 4a-c.The results indicated that the initial microstructure was homogeneous a result of heat treatment, and the grain size was about 6.43 μm.After the dynamic co pression, the grains suffered fragmentation, and the grain size decreased up to 5.51 μ and 5.3 μm after high strain rates of 1620 s −1 and 2820 s −1 , respectively.On the other ha deformation twins activated in the microstructure as a result of dynamic loading and p moted the increase in the strain rate.The morphology of the deformation twins show diversity under dynamic loading, including twin boundaries terminated at the gr boundaries, those terminated within the grains, and even the generated penetrating twi Meanwhile, a twin wafer-like microstructure was found in the sample subjected by d namic loading at 2820 s −1 .Figure 4d-f shows the kernel average misorientation (KAM) plot of the new alloy, which can represent the density distribution of the geometrically necessary dislocation (GND) boundaries macroscopically.Those boundaries with KAM > 0.5 • are considered as high-density dislocation boundaries (shown in green in the KAM plot), and those with KAM ≤ 0.5 • are considered as low-density dislocation boundaries (shown in blue in the KAM plot).In the initial state, high-density dislocations were rare and only existed as a result of previous heat treatment.However, the dislocation density of the sample increased significantly after dynamic loading, and dislocations were distributed not only at grain boundaries but also in grain interiors, which showed strong strain rate dependence.On the other hand, the fraction of low-angle grain boundaries (LAGBs) increased with the increase in the strain rate, and the fraction of LAGBs increased to 68.84% and 82.37% after the high strain rates of 1620 s −1 and 2820 s −1 , respectively.Some other relevant parameters of different state samples obtained through EBSD data statistics are listed in Table 4. Figure 5 shows the pole figures of the initial sample and the samples after the dynamic impact testing at 1620 s −1 and 2820 s −1 , respectively.The maximum texture intensity of the initial sample was 18.12.The sample after the impact testing with 1620 s −1 and 2820 s −1 showed a maximum texture intensity of 24.84 and 23.66 along the <0001> pole.Thus, more grains in the deformed samples must be aligned along the <0001> pole direction, demonstrating the large influence of the strain rate on the crystallographic texture evolution.
Crystals 2022, 12, x FOR PEER REVIEW 6 of 10 Figure 5 shows the pole figures of the initial sample and the samples after the dynamic impact testing at 1620 s −1 and 2820 s −1 , respectively.The maximum texture intensity of the initial sample was 18.12.The sample after the impact testing with 1620 s −1 and 2820 s −1 showed a maximum texture intensity of 24.84 and 23.66 along the <0001> pole.Thus, more grains in the deformed samples must be aligned along the <0001> pole direction, demonstrating the large influence of the strain rate on the crystallographic texture evolution.It is worth mentioning that the high-strength titanium alloy kept integrity and did not show any instability after dynamic loading, showing excellent comprehensive mechanical properties.The new Ti-6Al-1Mo-2Zr-0.55Fe-0.1Balloy is classified as the near-α titanium alloy according to the Kβ stability coefficient calculation [24].As is commonly It is worth mentioning that the high-strength titanium alloy kept integrity and did not show any instability after dynamic loading, showing excellent comprehensive mechanical properties.The new Ti-6Al-1Mo-2Zr-0.55Fe-0.1Balloy is classified as the near-α titanium alloy according to the K β stability coefficient calculation [24].As is commonly known, the α phase of a titanium alloy has a hexagonal close-packed (HCP) structure, with only three slip systems, but the dislocation slip on prismatic surfaces is facilitated to launch due to the c/a value (1.587) below the ideal HCP value (1.633).Furthermore, the addition of Al elements is considered to reduce the c/a value and benefit the dislocation movement [25][26][27].Additionally, an abundance of deformation twins released the dislocation pile-up and coordinated the plastic deformation of the alloy during the dynamic loading [28,29].On the other hand, the damage of materials under the dynamic loading was always related to the occurrence of adiabatic shear bands, which were considered to accompany the dynamic recrystallization process [30][31][32].In our investigation, the adiabatic shear bands have not been observed by optical microscopy and EBSD, and the content of recrystallized grains decreased seriously; even the imposed strain rate was equal to 2820 s −1 , as indicated in Table 4. Obviously, the novel titanium alloy has a good potential for the applications due to the simultaneous high strength and ductility, although the deformation mechanism still needs to be revealed further.

The Johnson-Cook Constitutive Equation
As mentioned above, when materials suffered high strain rate deformation, the plastic work generated from the deformation could be converted into heat energy, which increased the local temperature of materials.Theoretically, the temperature rise calculation was carried out by the following equation: where β is the ratio of the mechanical energy transferred into the thermal energy, generally taken as 0.9; W p is the plastic work; W p = ε i 0 σ i dε i , ρ is the material density; ρ = 4.45 g/cm 2 ; and C p is the constant pressure specific heat capacity of the material 0.526 J/g•K.The temperature rise of the new alloy at different strain rates can be obtained from the Equation (2); the result is presented in Figure 6.The fitting can be obtained as follows: Crystals 2022, 12, x FOR PEER REVIEW 7 of 10

The Johnson−Cook Constitutive Equation
As mentioned above, when materials suffered high strain rate deformation, the plastic work generated from the deformation could be converted into heat energy, which increased the local temperature of materials.Theoretically, the temperature rise calculation was carried out by the following equation: where β is the ratio of the mechanical energy transferred into the thermal energy, generally taken as 0.9; is the plastic work; = ∫ d , ρ is the material density; ρ = 4.45 g/cm 2 ; and is the constant pressure specific heat capacity of the material 0.526 J/g•K.The temperature rise of the new alloy at different strain rates can be obtained from the Equation ( 2); the result is presented in Figure 6.The fitting can be obtained as follows: Obviously, the temperature rises of the new alloy increase exponentially under the dynamic loading, especially when the strain rate exceeds 2000 s −1 .
where A, B, C, n, and m are coefficients to be determined; σ is the flow stress; ε is the equivalent plastic strain; and ̇ and ̇ are the reference strain rate and the equivalent plastic strain rate.* is the dimensionless temperature (T* = (T-T0)/(Tm-T0)), where , T, and are the reference temperature, the deformation temperature, and the melting point temperature of the material, taking = 293 K and = 1800 K.When ̇= 10 , = , for the compression experiment performed under quasi-static loading at room temperature, the equation can then be decoupled as follows: Obviously, the temperature rises of the new alloy increase exponentially under the dynamic loading, especially when the strain rate exceeds 2000 s −1 .
The thermal-viscoplastic constitutive model is commonly used to describe the dynamic mechanical response of metallic materials, such as the Johnson-Cook model, the Zerrilli−Armstrong model, and the Steinberg−Guinan model.Among them, the Johnson-Cook model is simple and can better describe the strain hardening, strain rate effects, and thermal softening effect of the material.In this paper, the Johnson-Cook model is used to describe the dynamic intrinsic structure of the new titanium alloy, and the model expression is as follows: where A, B, C, n, and m are coefficients to be determined; σ is the flow stress; ε is the equivalent plastic strain; and . ε 0 and .
ε are the reference strain rate and the equivalent plastic strain rate.T * is the dimensionless temperature (T* = (T − T 0 )/(T m − T 0 )), where T 0 , T, and T m are the reference temperature, the deformation temperature, and the melting point temperature of the material, taking T 0 = 293 K and T m = 1800 K.When . ε 0 = 10 −3 s −1 , T = T 0 , for the compression experiment performed under quasi-static loading at room temperature, the equation can then be decoupled as follows: It is rewritten as ln(σ − A) = ln B + n•ln ε, substituted into the stress−strain data under the quasi-static compressive loading at room temperature for linear fitting, and the final strain-hardening parameters are obtained as A = 1018 MPa, B = 774 MPa, n = 0.97.
The strain rate strengthening parameter C responds to the strain rate effect of the material and can be fitted using stress−strain data for different strain rates at room temperature, where the equation is as follows: Obviously, the value of C is the slope of σ/(1018 ), and after substituting the stress−strain data for different strain rates at room temperature, the value of the strain rate strengthening parameter C is 0.013.
Using the adiabatic temperature rise in Equation ( 5) plus the reference temperature as the deformation temperature, brought into Equation ( 6), the value of m is obtained by fitting it to the experimental data and taking the average value of 1.72.Then, the complete J−C constitutive equation is as follows: Figure 7 shows the results of the fitting of the experimental data of the alloy at high strain rates.The J−C constitutive equation constructed in this paper can effectively predict the mechanical response of the alloy under high strain rate deformation, especially in the plastic deformation stage.It is rewritten as ln(σ-A) = ln B + n•ln ε, substituted into the stress−strain data under the quasi-static compressive loading at room temperature for linear fitting, and the final strain-hardening parameters are obtained as A = 1018 MPa, B = 774 MPa, n = 0.97.
The strain rate strengthening parameter C responds to the strain rate effect of the material and can be fitted using stress−strain data for different strain rates at room temperature, where the equation is as follows: Obviously, the value of C is the slope of σ /(1018 + 777⋅ .)−1 = C⋅ln ( ̇ ̇), and after substituting the stress−strain data for different strain rates at room temperature, the value of the strain rate strengthening parameter C is 0.013.
Using the adiabatic temperature rise in Equation ( 5) plus the reference temperature as the deformation temperature, brought into Equation ( 6), the value of m is obtained by fitting it to the experimental data and taking the average value of 1.72.Then, the complete J−C constitutive equation is as follows: σ = (1018 + 774 • .) 1 + 0.013 ⋅ ln ̇ .
(1 − * .) (7) Figure 7 shows the results of the fitting of the experimental data of the alloy at high strain rates.The J−C constitutive equation constructed in this paper can effectively predict the mechanical response of the alloy under high strain rate deformation, especially in the plastic deformation stage.

Conclusions
(1) A novel near-α titanium Ti-6Al-1Mo-2Zr-0.55Fe-0.1Balloy was developed, which possesses simultaneous high strength (>1000 MPa) and ductility (>15%).(2) The strength of the alloy under dynamic loading enhanced significantly compared with the quasi-static compression and increased with the increase in the strain rate.An abundance of deformation twins released the dislocation pile-up and coordinated the plastic deformation of the alloy during the dynamic loading.(3) The Johnson-Cook constitutive equation was modified by the adiabatic temperature rise term, and a nonlinear fit was performed to construct a dynamic constitutive relationship at room temperature, which could describe the rheological behavior of the alloy under high strain rate conditions at room temperature.
The novel near-α titanium Ti-6Al-1Mo-2Zr-0.55Fe-0.1Balloy possesses excellent mechanical properties, a low-cost design, and good weldability, making it a good potential application in marine engineering.

Figure
Figure 4d-f shows the kernel average misorientation (KAM) plot of the new all which can represent the density distribution of the geometrically necessary dislocat (GND) boundaries macroscopically.Those boundaries with KAM > 0.5° are considered high-density dislocation boundaries (shown in green in the KAM plot), and those w KAM ≤ 0.5° are considered as low-density dislocation boundaries (shown in blue in KAM plot).In the initial state, high-density dislocations were rare and only existed a

Author Contributions:
Author contributions: conceptualization, C.Y. and Y.D.; methodology, Y.D. and C.Y.; validation, C.Y., Y.D. and I.V.A.; formal analysis, C.Y.; investigation, C.Y., H.C. and Y.D.; data curation, C.Y.; writing-original draft preparation, C.Y.; writing-review and editing, C.Y. and Y.D.; supervision, C.W., M.H., Y.D., H.C. and I.V.A.; project administration, I.V.A., H.C. and Y.D.; funding acquisition, Y.D. and H.C. All authors have read and agreed to the published version of the manuscript.Funding: The authors would like to gratefully acknowledge the support of the National Key Research and Development Program of China (No. 2021YFB3700802), the National Natural Science Foundation of China (No.51931008), the Ministry of Education of the Russian Federation (Project 0838-2020-0006), and the A Project, funded by the Priority Academic Program Development (PAPD) of Jiangsu Higher Education Institutions.