Effect of High Strain Rates on Adiabatic Shear Bands Evolution and Mechanical Performance of Dual-Phase Ti Alloy

In the present work, the adiabatic shear characteristics of our recently designed α + β dual-phase Ti alloy at different strain rates have been investigated by hat shaped specimen. The deformation process is divided into three stages: work hardening stage, steady stage, and unstable thermal softening stage. Along or near the shear deformation paths, the microvoids and the cracks can be captured at the strain rate of 1.8 × 104 s−1, 2.0 × 104 s−1, and 2.3 × 104 s−1, both of which contribute to the stable and unstable softening. It is found that dynamic stored energy of cold work will be significantly improved by the enhanced high strain rate. In the view of coupling analysis of inverse pole figure and grain boundary map, it seems that low angle grain boundaries present a good resistance to the formation of cracks and thermal softening. On the contrary, high angles grain boundaries are typically located in ASBs and their affecting regions, which is in line with the reported results. While the geometrical necessary dislocation (GND) density of adiabatic shear band (ASB) and its surroundings increased significantly, the width of the ASB becomes wider as the strain rate increases, which is consistent with the theory of sub-grain rotation dynamic recrystallization model. The formation of multiple ASBs in the corner position is schematically illustrated and the average elastic modulus and hardness of the ASB region are lower than the α and β phases, combined with the GND analysis, which proves that the ASB is a thermal softening zone in this experiment.


INTRODUCTION
Ti alloys are considered as ideal structural materials in aerospace and aircraft application, because of the characteristics of low density, high specific strength at both ambient and elevated temperatures, and excellent corrosion resistance (Lütjering and Williams, 2007). In the development of damagetolerance Ti alloys, a great number of theoretical and experimental research efforts have focused on the formation and evolution of shear bands (Zener and Hollomon, 1944;Anand and Spitzig, 1980;Kuriyama and Meyers, 1986;Marchand and Duffy, 1988;Needleman, 1989;Grady, 1992;Xue et al., 2005;Bronkhorst et al., 2006), criterion for the formation (Nguyen, 1997), microstructure, and phase transition in the shear bands formed under extreme conditions. In particular, under the high strain rate, the narrow-sheared regions generally undergo the severe plastic deformation with intense enhanced temperature in a short time, which will result in the microstructure evolution in local region to form the so-called adiabatic shear band (ASB). In general, ASBs are considered as threshold of mutation damage of metals under dynamic load (Meyers et al., 2001;Walley, 2007). Moreover, ASB will be yielded at the high strain rate attributing to the competition between thermal softening and strain/stress-rate hardening within the local regions (El-Azab, 2008;Rittel et al., 2008;Guo et al., 2019;Hao et al., 2021). Therefore, it is essential to investigate the strain-rate-dependent mechanical properties and structural evolutions of advanced metal materials (Rittel et al., 2008;Guo et al., 2019;Reddy et al., 2020), thus, to reveal the foundations of corresponding plastic deformation behaviours .
In the present work, effects of high strain rates on ASB evolution and mechanical performance of α + β dual-phase alloy (Lee and Lin, 1998) are investigated. The hat-shaped specimens are utilized to study the formation mechanisms of ASB under dynamic load by the separated Hopkison pressure bar (SHPB) technology, thus, to reveal the corresponding deformation and softening behaviors. The microstructure evolutions are characterized in terms of optical microscope (OM), scanning electron microscope (SEM), electron backscattered diffraction (EBSD), and transmission electron microscope (TEM). The investigations of the formation process of ASB can further reveal the dynamic damage process of materials and provide important references for preventing material failure and fracture during high-speed deformation and extending the service life of materials.

MATERIALS AND METHODS
In the present work, the hat-shaped specimens of the annealed forging α + β dual-phase Ti alloy was deformed at ambient temperature by means of separated Hopkinson pressure bar (SHPB), which conventionally captured the well-controlled and designed localized shear in the study of large strain and high strain rate deformation. The geometry of hat-shaped specimen together with their sections of investigated ones are presented in Figure 1. In order to avoid premature fracture failure of the sample and show more early behaviors of shear localization, the configuration of Hat with an outer diameter larger than inner diameter of Brim ring is selected. The dynamic compression test was carried out on a Φ14.7 mm diameter separated Hopkinson compression rod in the Dynamic Mechanics Laboratory of Beijing Institute of Technology, and the stress-strain curve under the condition of high strain rate was obtained. The detailed information about the system of experimental device including impact, bar incident bar, and transmitted bar can be found in our previous reports . Through adjusting the air pressure of the incident bar to 0.60 atm, 0.80 atm, and 0.90 atm separately, the different strain rates and their stress-strain curves were obtained at the strain rate of 1.8 × 10 4 s −1 , 2.0 × 10 4 s −1 , and 2.3 × 10 4 s −1 , respectively. Afterwards, the hat-shaped specimens were cut along the axis to trace the shear paths and the deformed microstructures.
The microstructure evolutions are characterized in terms of OM, SEM, EBSD, and TEM. Optical microstructure is observed by Nikon Eclipse LV150N optical microscope. The EBSD analysis is executed on field emission SEM of JEOL 7800F with the acceleration voltage at 20 kV, the probe current of 14 nA, and the scanning speed of 815 Hz . It is worth mentioning that the size of scanning step is 0.15 m for the area of 0.16 mm 2 , which is 1 m for the area of 2.88 mm 2 .
Based on the model of the hat-shaped specimen proposed by Andrade et al., the shear parameters including shear stress τ s , shear strain γ s and shear strain rate _ γ s can be calculated by the following equations (Andrade et al., 1994).
Here, the outside diameter of hat and inner diameter of brim are expressed as d 0 and d 1 , respectively. C 0 is the elastic wave speed and E 0 is Young's modulus of the Hopkinson bars. A s and A b represent the areas of the shear section and the cross section of transmitted bar. Correspondingly, the elastic strains of incident and transmitted bars are ε i and ε t , separately. It can be found that the severe shear strain can be obtained in the designed shear region, which is convent to capture the local shear deformation process and microstructure evolution . In order to calculate the width of ASB, the model reported by Grady and Kipp (Kipp and Grady, 1985;Grady, 1992;Landau et al., 2016) is utilized, which takes into account the energy dissipation in the process of ASB and can be expressed as: where ρ is the density, C the heat capacity, χ the thermal diffusivity, τ b the flow stress, and _ γ the shear strain rate. The (zτ/zθ) is the thermal softening coefficient, which is obtained from the work of Shahan and Taheri (1993). The material parameters were from the database of the Metflow software (Mitchell, 2007). Figure 2 presents the typical microstructures of the as-received dual-phase Ti alloy (Lee and Lin, 1998) fabricated by Western Superconducting Material Technology Co., Ltd., which was forged at 920°C and annealed at T β of 960°C afterward. The classical microstructures consisted of equiaxed α p with average size of about 10 μm and coalesced secondary alpha phases (α s ) with thickness of about 0.9 μm. The phase fractions of α p phases is about 46.2%. Figure 3 shows the shear stress-shear strain response of hatshaped specimens utilized in SHPB test at high strain rates of 1.8 × 10 4 s −1 , 2.0 × 10 4 s −1 , and 2.3 × 10 4 s −1 . Referring to the static compression test, the stress-strain curve at high strain rate consisted of four stages, including the elastic deformation region, the strain hardening, the stbale softening, and the unstable softening. In particular, at the strain rate of 1.8 × 10 4 s −1 , this alloy presents a maximum shear stress as high as 2016 MPa at the plastic deformation stage, indicating an excellent damage tolerance capability, as shown in Figure 3A. The shear stress increases with the improved shear strain and reaches a maximum as high as 2230 MPa with the shear strain of 0.123. In the range of shear strain from 0.123 to 0.165, the shear stress slowly decreased from the peak by 118 MPa attributing to the thermal softening during the adiabatic shear. It is worth mentioning that the dynamic stored deformation energy till to the work hardening stage can be characterized as the integration of the stress-strain curve.

RESULTS AND DISCUSSION
While Figures 3B,C show the stress-strain curve obtained at the higher strain rates of 2.0 × 10 4 s −1 and 2.3 × 10 4 s −1 , their systematic comparations referring to the static ones are presented in Figure 3D. At the strain rate of 2.0 × 10 4 s −1 , the shear stress increases with the improved shear strain and reaches a maximum as high as 2267 MPa with the shear strain of 0.111. In the range of shear strain from 0.111 to 0.143, the shear stress slowly decreased by 102 MPa from the peak attributing to the thermal softening during the adiabatic shear. When the strain reaches 0.217, the curve shows a plateau. On the contrary, the stress rapidly reaches the maximum under the strain rate of 2.3 × 10 4 s −1 , and the strain strengthening and thermal softening effects in the plastic strain stage balance each other, as shown in Figure 3C. The stress reaches a peak of 2235 MPa at the strain of 0.099. The curve shows a plateau at the strain of 0.202, highlighting the thermal softening behaviors. It can be seen that the higher strain rate will result in the smaller plastic strain and strain to reach the peak stress, as displayed in Figure 3D. Moreover, it is found that dynamic stored energy of cold work (Rittel et al., 2008;Landau et al., 2016;Baik et al., 2021) will be significantly improved by the enhanced high strain rate, which are 393 MJ m −3 , 524 MJ m −3 , and 775 MJ m −3 for the strain rate of 1.8 × 10 4 s −1 , 2.0 × 10 4 s −1 , and 2.3 × 104 s −1 , respectively. Therefore, the dynamic recrystallization and ASB-mediated dominated softening mechanisms should be discussed. In order to reveal aforementioned stable and unstable softening mechanisms, the multi-scales SEM characterizations of ASBs in the hat-shaped specimen at these three strain rates are shown in Figures 4-6, respectively. The additional numbers identify the typical features of selected regions. Under the shock loading conditions, the primary α phase on both sides of ASB is elongated and deformed along the shear direction,  locating at transition area near the centre of the shear band and the matrix, as shown in Figures 4-6. Generally, the ASBs of the hat-shaped sample will start from the upper corner or the lower corner, which are mainly located at the α/β dual-phase colony structures. Along or near the shear deformation paths, the microvoids and the cracks can be captured at various strain rates, both of which contribute to the stable and unstable softening, as shown in Figures 4B-4, Figures 5A-5, B-4, and Figures 6B-5. It is understood that those microvoids are the preferred sites for nucleation and growth of cracks. When increasing the strain rate from 1.8 × 10 4 s −1 to 2.3 × 10 4 s −1 , the width and length of microcracks are improved dramatically. Moreover, the width of ASB locating the main shearing/cracking path is dramatically enhanced by the increased strain rate, which  is attributed to the higher dynamic stored energy of cold work than those at lower strain rate. Comparing to the width of ASB at 1.8 × 10 4 s −1 , they are estimated to be 5-10 μm at 2.0 × 10 4 s −1 and larger than 10 μm at 2.3 × 10 4 s −1 based on the Grady-Kipp model expressed as Eq. 4. Furthermore, with the improved strain rate, the anomaly microstructural evolutions in the ASBs can be captured, which can be changed from the linear ASBs to the bowing vortex structures caused by the rotations of sub-grains and grains, as presented in Figures 6B-4, B-5.
Taking the advantages of EBSD characterizations, the full scans of ASBs and the corresponding affecting zones in terms of the BC map, the geometrically necessary dislocation (GND) map, and the coupling analysis of IPF + GB at these three different strain rates are presented in Figures 7-9, respectively. The thickness of ASB affected zone resulting in the collaborating plastic deformation can be clearly captured by GND mapping. It can be seen that the GND density of ASB and its surroundings increased significantly when improving the strain rate, which also highlight the effect zone of ASBs. As dislocation density increases, dislocation entanglement forms a dislocation network, which is often considered a sign of work hardening. In fact, ASB eventually evolves into a softened area, during which thermoplastic instability occurs. When the material is under dynamic load, the heat generated by deformation cannot be transferred out in time to form a local "adiabatic temperature rise," and the temperature rise causes the material to soften. When the softening effect is greater than the work hardening effect, a softened area will appear as the final observed adiabatic shear zone. Moreover, in the view of coupling analysis of inverse pole figure and grain boundary map (IPF + GB), it seems that low angle grain boundaries present a good resistance to the formation of cracks and the thermal softening. On the contrary, high angles grain boundaries are typically located in ASBs and their affecting regions, which is in line with our previous works  and the reported one in Ti (Timothy and Hutchings, 2013). With the guidance of grain boundary complexions (Grebe et al., 1985;Da Silva and Ramesh, 1997;Sun et al., 2014a), it is understood that the free volumes exist at the boundaries, constructing the weak bonded regions and contributing to the initiation of ASB.
It is believed that dynamic recrystallization can be almost universally observed in the microstructure of ASBs (Rittel et al., 2008). The fine equiaxed sub-grains in the ASB are formed by dynamic recovery and continuous dynamic recrystallization (Yang et al., 2011a). As shown in Figure 10, the microstructures of the bottom corner position of shear region in left side of specimen are presented in terms of BC mapping and IPF mapping. Multiple very narrow ASBs can be observed in the BC map, as highlighted by those dash lines in Figure 10. It is worth mentioning that the multiple adiabatic shear bands in hatshaped specimens during SHPB test are rarely reported, which can be captured in metallic materials during other dynamic impact tests, such as explosive collapse of a thick-walled cylinder (TWC) (Chichili et al., 1998;El-Azab, 2008) and ballistic impact test (Shahan and Taheri, 1993;Yang and Wang, 2006). Meanwhile, the un-indexable regions show more clearly the positions of multiple very narrow ASBs, where there are a great amount ultra-fine equiaxed sub-grains. Since one of them is found at the original bottom corner position of the sample before the plastic deformation, it is indicated that the formation of multiple ASBs is caused by the dramatic change of stress concentration in the bottom corner of the specimen. Therefore, multiple ASBs tend to be near parallel distributed along the shear direction, attributing to the concentrated plastic deformation in relatively narrow banded region near the bottom corner of the hat-shaped specimen during dynamic impact. Those regions  between the adjacent very narrow ASBs presents stronger shear deformation microstructural characteristics than other regions. Moreover, according to the subgrain rotation dynamic recrystallization model (Meyers et al.), ASBs generate in metallic materials through four steps: (1) dislocations proliferate and distribute randomly during the initial stage of deformation; (2) dislocations rearrange to form elongated dislocation cells, known as the dynamic recovery; (3) elongated sub-grains generate from the dislocation cells as the deformation continues; (4) elongated sub-grains dissolve and rotate into equiaxed recrystallized micrograins.

CONCLUSION
In summary, the adiabatic shear localization behavior of hatshaped sample of α + β dual-phase Ti-6Al-2Cr-2Mo-2Nb-2Sn-2Zr alloy is investigated by SHPB test. Under the shock loading conditions, the primary α phase on both sides of ASB is elongated and deformed along the shear direction, locating at transition area near the centre of the shear band and the matrix. Generally, the ASBs of the hat-shaped sample will start from the upper corner or the lower corner, which are mainly located at the α/β dual-phase colony structures. Along or near the shear  Frontiers in Materials | www.frontiersin.org February 2022 | Volume 8 | Article 808244 8 deformation paths, the microvoids and the cracks can be captured at various strain rates, both of which contribute to the stable and unstable softening. It is found that dynamic stored energy of cold work will be significantly improved by the enhanced high strain rate, which are 393 MJ m −3 , 524 MJ m −3 , and 775 MJ m −3 at the strain rate of 1.8 × 10 4 s −1 , 2.0 × 10 4 s −1 , and 2.3 × 10 4 s −1 , respectively. In the view of coupling analysis of inverse pole figure and grain boundary map, it seems like that low angle grain boundaries present a good resistance to the formation of cracks and the thermal softening. On the contrary, high angles grain boundaries are typically located in ASBs and their affecting regions, which is in line with the reported results. The GND density of ASB and its surroundings increased significantly when improving the strain rate, which also highlight the effect zone of ASBs.

DATA AVAILABILITY STATEMENT
The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

FUNDING
This study received funding from the Science Challenge Project, grant number TZ2018002, and the Western Superconducting Technologies Co., Ltd., EPRCTC project 41422010505. The funder was not involved in the study design, collection, analysis, interpretation of data, the writing of this article or the decision to submit it for publication.