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Quasi-static and dynamic forced shear deformation behaviors of Ti-5Mo-5V-8Cr-3Al alloy
Materials Science & Engineering A 691 (2017) 51–59
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Quasi-static and dynamic forced shear deformation behaviors of Ti-5Mo5V-8Cr-3Al alloy
MARK
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Zhiming Wang, Zhiyong Chen , Congkun Zhan, Lianjun Kuang, Jianbo Shao, Renke Wang, Chuming Liu School of Materials Science and Engineering, Central South University, Changsha 410083, China
A R T I C L E I N F O
A BS T RAC T
Keywords: Ti-5Mo-5V-8Cr-3Al alloy Forced shear deformation Adiabatic shear band Microtexture Hardness
The mechanical behavior and microstructure characteristics of Ti-5Mo-5V-8Cr-3Al alloy were investigated with hat-shaped samples compressed under quasi-static and dynamic loading. Compared with the quasi-static loading, a higher shear stress peak and a shear instability stage were observed during the dynamic shear response. The results showed that an adiabatic shear band consisting of ultrafine equiaxed grains was only developed in the dynamic specimen, while a wider shear region was formed in the quasi-static specimen. The microhardness measurements revealed that shear region in the quasi-static specimen and adiabatic shear band in the dynamic specimen exhibited higher hardness than that of adjacent regions due to the strain hardening and grain refining, respectively. A stable orientation, in which the crystallographic {110} planes and < 111 > directions were respectively parallel to the shear plane and shear direction, developed in both specimens. And the microtexture of the adiabatic shear band was more well-defined than that of the shear region in the quasistatic specimen. Rotational dynamic recrystallization mechanism was suggested to explain the formation of ultrafine equiaxed grains within the adiabatic shear band by thermodynamic and kinetic calculations.
1. Introduction Adiabatic shear band (ASB) is an important deformation mode that intensive deformation localizes in a narrow band when metal deformed under dynamic loading [1]. It is generally recognized that the formation of shear band is a result of the effect of thermal softening exceeding that of strain and strain rate hardening [2,3]. With the formation of the shear band, the bearing capacity of structural material would decrease sharply and even lead to a catastrophic failure because cracks always nucleate and propagate within the ASB [3–5]. Meanwhile, the investigation on quasi-static experiment contributes to a better understanding of the dynamic deformation, and low strain rate deformation is frequently involved during the processing and application of metallic material. Thus, much attention has been paid to exploring the mechanical behavior and microstructure development in various metals and alloys during quasi-static and dynamic deformation. Some experimental and simulation studies [4–6] have revealed that the shear stress is related to the strain rate and the dimensions of hat-shaped specimen. The mechanical curve of hat-shaped specimen deformed under quasi-static loading presents a continuous hardening characteristic, and yet a stress collapse would take place on dynamic shear response. It has been reported that titanium and its alloys are
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Corresponding author. E-mail address: [email protected] (Z. Chen).
http://dx.doi.org/10.1016/j.msea.2017.03.005 Received 21 January 2017; Received in revised form 1 March 2017; Accepted 2 March 2017 Available online 08 March 2017 0921-5093/ © 2017 Elsevier B.V. All rights reserved.
very susceptible to form ASB during dynamic deformation due to their poor thermal conductivity [7,8]. Numerous studies on titanium and its alloys have revealed that the microstructure of ASB consists of ultrafine equiaxed grains, which is a result of dynamic recrystallization [8–13]. Based on this remarkable feature and an extremely short deformation time, a new mechanism named as rotational dynamic recrystallization (RDRX) was proposed by Meyers et al. [14]. It has also been reported that a well-developed shear band would not be formed under the dynamic condition, but the shear localization is more pronounced in the dynamic specimen than that in the quasi-static specimen [15]. Grains adjacent to the ASB represent a special orientation variation that the crystallographic {110} planes and < 111 > directions respectively tend to parallel to the shear plane and shear direction in Ta and Ta-W alloys [16] and stainless steel [17] (body-centered cubic structure metals). Dougherty et al. [18] indicated that the grains within the ASB in steel show three type orientations: {112} < 111 > , {110} < 111 > and {110} < 001 > . These well-defined simple shear texture formed in the dynamic specimen implies that dislocation slip in the {110} and {112} planes along the < 111 > directions. Additionally, Bhattacharyya et al. [19] reported that the deformation texture appears sharper for dynamic specimen compared with quasi-static specimen at large strains ( > 1.0). Thus, the strain rate is an important factor to affect
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3. Results and discussions
the mechanical property, microstructure and microtexture development of metals. Ti-5Mo-5V-8Cr-3Al alloy is a kind of typical metastable beta titanium alloy, which would experience different strain rate deformations during its service lifespan. However, the research on the mechanical response, microstructure and microtexture characteristics of beta titanium alloys deformed under quasi-static and dynamic forced shear conditions is still scanty. In this paper, we investigated the forced shear deformation behaviors of Ti-5Mo-5V-8Cr-3Al alloy under quasi-static and dynamic conditions, and focused on the deformed microstructure and microtexture features. Additionally, the thermodynamic and kinetic calculations were performed to verify the RDRX mechanism. The findings in this work advance our understanding of the force shear deformation behaviors of Ti-5Mo-5V-8Cr-3Al alloy under quasi-static and dynamic loading.
3.1. Shear stress-shear strain curve According to Longère et al. [4], the shear stress (τ) and shear strain (γ) of quasi-static and dynamic forced shear deformation can be calculated by the following equations:
τ=
F Sshear
(1)
γ=
ΔL Wshear
(2)
Sshear =
π D+d D−d 2 ( ) + H2 cos α 2 2
α = arctan
2. Experimental
D−d 2H
(3) (4)
where F is the load applied on the specimen, ΔL is the relative displacement of the top and bottom end. Sshear and Wshear are the section area and width of the shear region, respectively. D and d are top and bottom diameter of the hat-shaped specimen, respectively. α is the angle between shear direction and loading axis. H is the shear region height. The shear stress-shear strain curves of Ti-5Mo-5V-8Cr-3Al alloy during quasi-static deformation at the strain rate of approximately 1.0×10−3 s−1 and dynamic deformation at the strain rate of approximately 6.3×104 s−1 are shown in Fig. 3. The compression displacements (ΔL) in these two tests are the same. Therefore, the shear strain (γ) of the dynamic deformation was larger than that of the quasi-static deformation because the width of the shear region (Wshear) in the dynamic specimen was smaller. The two curves are quite different, except for a similar elastic region. The shear stress of quasi-static sample increased with the increasing strain after the yield point due to the strain hardening, but the rate of strain hardening decreased gradually. The dynamic curve can be divided into three stages as the denoting point (a, b, c, d) in Fig. 3. In the first stage (a-b), the shear stress increased with the increasing shear strain. In the second stage (b-c), the shear stress started to decline with the increasing shear strain. Hence, the shear stress (point b) reached the maximum value of 960 MPa at the shear strain of 0.61. According to the maximum stress criterion for instability deformation [20], the point b represented the onset of unstable deformation, after which the deformation began to localize into an ASB. In the third stage (c-d), the shear stress varied slightly and a “plateau” was formed due to the competing process of the work hardening and the thermal softening introduced by significant rising temperature.
The forged Ti-5Mo-5V-8Cr-3Al alloy plate with dimensions of 200 mm×80 mm×60 mm was kept at the temperature of 1203 K (930 °C) for 55 min, and subsequently the thick sheet was hot-rolled from 60 to 12 mm, yielding a cumulative rolling reduction of 80%. The initial microstructure of hot-rolled Ti-5Mo-5V-8Cr-3Al alloy plate is shown as the 3D view in Fig. 1, where strip grains were observed in the hot-rolled plate. The tested hat-shaped specimens, whose dimensions are shown in Fig. 2(a), were fabricated with loading axis paralleling to the normal direction of the titanium alloy plate. The quasi-static (~10−3 s−1) and dynamic (~104 s−1) forced shear deformation were performed by an Instron apparatus and a SHPB system at room temperature. Specimens for microstructure characterization were cut from the deformed hat-shaped samples along the loading axis by means of electrical discharge machining. The sectioned surfaces for metallographic observation were polished to a mirror finish and then etched with 2 ml HF+15 ml HNO3+83 ml H2O. Vickers microhardness was obtained using an HVS-1000 Microhardness Tester with a load of 50g and a dwell time of 10 s. Specimens for electron backscatter diffraction (EBSD) measurement were prepared by mechanical polishing and electro polishing using a solution of 60 ml HClO4+360 ml CH3(CH2)3OH+600 ml CH3OH on Automatic TwinJet-Electro polishing device at 75 V and −30 °C. EBSD observations of the electrolytic polishing region (Fig. 2(b)) were carried out on a FEI Sirio200 scanning electron microscope system with an acceleration voltage of 20 kV. Microstructure and microtexture were also analyzed by available commercial TSL-OIM Version 5.0 software.
3.2. Microstructure characteristic and microhardness ND
An enlarged optical micrograph of the shear region (Fig. 2) in the quasi-static and dynamic specimen was respectively shown in Fig. 4(a) and (b). As marked in Fig. 4, the left ends were the top ends of the hatshaped samples and the right ends were the corresponding bottom ends. As shown in Fig. 4(a), the plastic deformation of quasi-static specimen mainly occurred in a broad region named as shear localization region. The grains within this region were deformed and elongated toward the shear direction (SD), while those outside the region basically kept the original features. It should be also noted that groups of band structures (denoted by some white arrows) located in some grains. In beta titanium alloys, generally, the thin bands are formed due to the dislocation slip [21]. The shear localization region can be preliminary identified as the region between two black dashed lines and its width was approximately 600 µm. Additionally, the distribution of bands revealed that the inhomogeneous deformation within the shear region. The grains of the bottom end experienced more shear deforma-
TD RD Top end
Bottom end Fig. 1. Microstructure of the initial hot-rolled Ti-5Mo-5V-8Cr-3Al alloy plate. ND, RD and TD respectively stand for the normal direction, rolling direction and transverse direction of the hot-rolled plate.
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(a)
(b) Top end
Shear region
Bottom end
Fig. 2. Schematic illustration of hat-shaped sample and specimen preparation for EBSD in the deformed hat-shaped sample: (a) hat-shaped sample, (b) the region for EBSD observation. SD, SPN and ND respectively stand for the shear direction, shear plane normal and section plane normal.
quasi-static specimen, while the case in the dynamic specimen was inverse, which can be related to the distinct stress states in the two specimens [22]. In order to further understand the forced shear deformation behaviors of Ti-5Mo-5V-8Cr-3Al alloy, microstructure (including grain size, grain morphology and grain orientation) was also characterized by EBSD technique. The orientations of grains were represented by an inverse pole figure color code, in which the red, blue and green respectively represented < 001 > , < 111 > and < 101 > direction. The low angle grain boundaries (LAGBs) with misorientation of 2°– 15° and the high angle grain boundaries (HAGBs) above 15° were represented by white and black lines, respectively. Kernel Average Misorientation (KAM) investigation was used to determine the local values of strain energy with calculation parameter at the fifth nearest neighbor pixels and a maximum misorientation angle of 5°. The black regions in maps were those areas where no orientation data could be acquired by EBSD technique. Fig. 5, with a scanning step size of 4 µm, exhibits the EBSD micrographs of shear localization region adjacent to the top end of the quasi-static specimen. The black regions located in the middle part of IQ map (Fig. 5(a)). It could be obviously seen that grains were deformed to generate groups of parallel band structures, which was similar with the optical microcopy observation (Fig. 5(a)). The KAM map (Fig. 5(b)) clearly shows that the plastic strain mainly occurred in the shear region (indicated by red and yellow color).Fig. 5(c) is an inverse pole figure colored orientation map with respect to the shear plane normal (SPN) to exhibit the deformed microstructure. With the shear deformation, grains in both sides were elongated toward the core of the shear region while the directions were opposite. The shear deformation in the right side was more inhomogeneous than that in the left side. Grains in the left side experienced a certain deformation but kept the original orientation, while the shear deformation in the right side was enough to change grains orientation. Therefore, the variation of grains color was more obvious in the right side. The shear region in Fig. 5(c) can be roughly divided into two regions (marked with A and B) for further analysis of microtexture evolution. In the region A, which was far away from the core of the shear region, the grains were slightly deformed and maintained the original characteristic. In the region B, which was the middle area of the shear region, the grains were severely elongated and fragmentized. Two arrows (L1 and L2) were marked in a strip grain and the corresponding misorientation traces were shown in Fig. 5(d). Along the black arrow, the misorientation between neighboring points in the grain did not exceed 6°, while the point-to-origin misorientation continuously increased with the increasing distance. This can be associated to the formation of geometrically necessary dislocations required to accommodate plastic deformation gradients
Fig. 3. Shear stress-shear strain curves of Ti-5Mo-5V-8Cr-3Al alloy during quasi-static and dynamic deformation. (a) Shear locaalization regiion
Ban nd structures
Bottom ennd
Top end
(b) Ad diabatic shear band Top end
Bottom end B
Fig. 4. Optical micrographs of the shear region in the hat-shaped specimen after: (a) quasi-static loading, (b) dynamic loading.
tion than that of the top end. In the dynamic specimen (Fig. 4(b)), the plastic deformation was highly localized in a narrow band named as ASB. The ASB was straight and its width was approximately 40 µm. The propagated direction of the ASB was the maximum shear stress direction – SD. The microstructure within the ASB was not visible via optical microcopy. Grains adjacent to the ASB were elongated toward the band. Consequently, a certain amount of plastic deformation also took place outside the ASB. The microstructure away from the ASB consisted of original coarse grains with little deformation. Besides, the crack at the bottom end was longer than that at the top end in the 53
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Fig. 5. EBSD micrographs of quasi-static deformation specimen (step size: 4 µm): (a) IQ map; (b) KAM map; (c) IPF colored orientation map with respect to SPN; (d) the misorientation profile measured along lines L1 and L2 in (c); (e) inverse pole figure of SPN showing the variation of crystal orientation along the black arrow in (c).
of LAGBs with grains close to the core of the shear region. Fig. 6, with a scanning step size of 3 µm, shows the microstructure of dynamic specimen. The forced shear deformation mainly localized in the ASB (the black area in Fig. 6(a)) which crossed many grains and subdivided the image into two parts. Meanwhile, the strain of grains outside the ASB was well illustrated in the KAM map (Fig. 6(b)). It could be seen that the plastic strain in the left map was larger than that in the right side. As shown in Fig. 6(c), the grains adjacent of the ASB were elongated toward the SD and fragmented. Based on the distribution of LAGBs and the varying color within grains, the deformation mechanism is dislocation slip. Fig. 6(d) shows the detailed misorientation angles measured in grain A and B (in Fig. 6(c)). The maximum misorientation angle between neighboring points along lines L1 and L2
along the black arrow in the strip grain [23]. In contrast, the misorientation trace along the red arrow changed dramatically when it crossed several high angle grain boundaries. Hence, the strip grain was observed to be fragmented along the red arrow direction as a consequence of deformation mainly concentrated on these HAGBs. Meanwhile, the varying color in the strip grain implied lattice rotations. The crystal orientation corresponding to points 1–10 was respectively labeled as 1–10 in Fig. 5(e). It was easy to find that great changes have taken place in the crystal orientation of the strip grain. As the blue arrow indicated, the crystallographic plane paralleling to shear plane gradually transformed from a {111} plane into a {110} plane. The profuse color variation (or orientation) within grains indicated extensive dislocation slip, which was also indicated by the increasing number 54
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Fig. 6. EBSD micrographs showing the microstructure of dynamic specimen (step size: 3 µm): (a) IQ map, (b) KAM map, (c) IPF colored orientation map, (d) the misorientation profile measured along line L1 and L2 in (c).
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Fig. 7. EBSD micrographs of the adiabatic shear band in the dynamic specimen (step size: 50 nm): (a) IQ map; (b) IPF colored orientation map; (c) the grain size distribution map; (d) the misorientation angle map; (e) enlarged view of an area of (b), black arrows indicate the HAGBs; (f) the misorientation profile measured along line L in (e).
grain size is about 0.25 µm). The misorientation angle map (Fig. 7(d)) shows the distribution of identified grain boundaries angle. In short, Fig. 7(a)-(d) reveal that the microstructure within the ASB consisted of equiaxed ultrafine grains with low dislocation density and well defined high-angle grain boundaries. Besides the equiaxed grains bounded by HAGBs, some elongated large grains were observed in the ASB. Fig. 7(e) gives an enlarged view of an elongated grain (marked by red dotted oval) of Fig. 7(b). This grain was surrounded by HAGBs (black lines) and divided by LAGBs (white lines) inside or among the fragmentized grains. The LAGBs would further evolve into HAGBs
was 1° and 4.5°, and the accumulative misorientation angle was 9° and 18°, respectively. This means the stored energy of grain B is much higher than that of grain A because of grain B is nearer to the shear band. Fig. 7 shows the EBSD micrographs were obtained from the inside of the ASB in the dynamic specimen by high-resolution EBSD scanning (step size: 50 nm). As shown in Fig. 7(a), the microstructure within the ASB was composed of ultrafine equiaxed grains. In Fig. 7(b), most grain colors were blue and green, and a large amount of HAGBs and LAGBs can be seen. Fig. 7(c) shows the grain size distribution (average 56
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Fig. 10 shows the microtexture of the grains in the dynamic specimen. As shown in the IPFs of SD, the intensity around < 001 > direction weakened obviously while the < 111 > component had a pronounced increase. In the IPFs of SPN, the < 001 > component disappeared and the intensity of < 112 > direction decreased, while a concentrating peak arose in the < 101 > direction. It reveals that most of grains within the ASB have their {110} planes and < 111 > directions respectively parallel to the shear plane and shear direction. The microtexture characteristic was in accord with the grains color in Fig. 8(b). Compared with the microtexture development in quasi-static specimen, a well-defined texture formed during the dynamic deformation due to a higher strain occurred in the ASB. Moreover, it could be concluded that the predominant mechanism operating during forced shear deformation in Ti-5Mo-5V-8Cr-3Al alloy specimen is dislocation slip in the {110} planes along the < 111 > directions. Fig. 8. Vickers microhardness of the quasi-static and dynamic specimen.
3.4. Adiabatic temperature rise and dynamic recrystallization with further deformation. Actually, some parts of LAGBs, as indicated by four black arrows in Fig. 7(e), have transformed into HAGBs. The gradual transformation process is regarded as subgrain rotation nucleation stage in continuous recrystallization [24], which results in the high fraction of HAGB in the shear band, as shown in Fig. 7(d). Fig. 7(f) displays the point-to-point and point-to-origin misorientation angle variation along line L in the elongated grain. The point-to-point curve shows that there are three misorientation jumps (indicate the locations of LAGBs) for the pileup of dislocations, which allows the definition of several separated regions within the grain. Fig. 8 shows the average Vickers microhardness of the dynamic and quasi-static specimens. It should be noted that the microhardness values of the two specimens decreased from the middle of shear region to the matrix. The decreasing rate in the dynamic specimen was greater than that in the quasi-static specimen. This indicates that the width of the shear region in quasi-static specimen is much smaller than that in the quasi-static specimen, which is in accord with the above microstructure observations. As reported [11], high microhardness can be attributed to the strain hardening and grain refining. It is worth mentioning that the indentation size was slightly smaller than the width of the ASB to obtain a microhardness of the ASB. And the size of indentation was much smaller than the average grain size in the shear localization region and the outside ASB. Therefore, higher microhardness in the shear localization region and the vicinity of the ASB should be mainly attributed to the strain hardening. The highest microhardness was obtained in the ASB due to the grain refining.
Under the quasi-static condition, the loading time was sufficient to dissipate the heat generated by deformation. While, the heat generated by the localized plastic deformation cannot dissipate during the short dynamic loading duration. Thus, the dynamic deformation process can be regarded as adiabatic in perspective of thermodynamic. And the temperature (T) within ASB can be calculated by the following equation [25]:
T=
β Cνρ
∫0
γ
τ dγ + T0
(5)
where β is the fraction of plastic work converted into heat (assumed to be a constant 0.9 in this case [3]) and T0 is the ambient temperature (298 K). ρ is the mass density (4810 kg/m3), and Cν is heat capacity (542 J/K) of Ti-5Mo-5V-8Cr-3Al alloy [26]. The calculation revealed that the temperature in the shear region of hat-shaped specimen increased with the increasing shear strain. With the increasing temperature, the effect of thermal softening exceeds that of strain and strain rate hardening. Thus, as shown in Fig. 3, a shear instability stage was observed on the dynamic shear stress-shear strain curve. Meanwhile, the theoretically maximum temperature of the ASB can reach ~1330 K which was well above the temperature for dynamic recrystallization of 940 K (~0.5 Tm, Tm is the melting point). Therefore, the equiaxed ultrafine grains with high-angle boundaries observed by EBSD (Fig. 8) should be a product of dynamic recrystallization. Hines et al. [25] pointed out that the traditional dynamic recrystallization mechanisms are excessively slow in kinetic time to account for the formation of recrystallized grains during high-strain-rate deformation. Considering the recrystallization kinetic time, the rotational dynamic recrystallization mechanism proposed by Nesterenko and Meyers [14,27] is reasonable to account for the formation of recrystallization grains within ASB. Hence, the kinetic calculation can be described by the following equation [17,27]:
3.3. Microtexture characteristic It is well accepted that the predominant deformation of hat-shaped samples is shear. Shear textures are conventionally defined in terms of the crystallographic plane {hkl} and direction < uvw > , parallel to the shear plane and shear direction, respectively [6,9,11,16–18]. The microtextures of region A and B in Fig. 5(c) were calculated and illustrated in the inverse pole figures (IPFs) of SD and SPN. In Fig. 9, the IPFs of SD show grains orientation did not undergo obvious change from the original orientations. Thus, the orientation that < 111 > and < 112 > directions parallel to SD has already been stable. On the contrary, the IPFs of SPN show an obvious microtexture variation. The concentrative peak of grain orientation changed from < 111 > to < 101 > direction with the decreasing distance to the core of the shear localization region, and a weak peak around < 112 > was retained. Thus, most of grains in the shear region showed their crystal plane paralleling to the shear plane changes from the {111} planes to the {110} planes during the plastic deformation, and some grains retained their original orientation that the {112} planes parallel to the shear plane. It is consistent with the microtexture evolution of the strip grain in Fig. 5(c).
3 tan θ − 2 cos θ 3 − 6 sin θ
=
−
4 3 9
4δηD exp(−Q / RT ) t LKT
ln
2+ 3 2− 3
+
2 3
+
4 3 9
ln
tan(θ / 2) − 2 − 3 tan(θ / 2) − 2 + 3
(6)
where θ is the rotation angle for subgrain boundaries (0°–30°), L is the average diameter of subgrain, K is the Boltzmann constant, T is the temperature in shear band, t is the time, δ is the grain boundary thickness, η is the grain boundary energy, D is the grain boundary diffusion coefficient, Q is the activation energy of grain boundary diffusion. There is no kinetic parameter of Ti-5Mo-5V-8Cr-3Al alloy currently, so the kinetic parameters of another beta titanium alloy, Ti5Al-5Mo-5V-1Cr-1Fe, are referred [28]: δ=5.8×10−10 m, η=1.19 J/m2, D=2.8×10−5 m2/s, Q=156 kJ/mol, R =8.314 J/(K mol), K=1.38×10−23 J/K. The kinetic calculation results, shown in Fig. 11, predict significant 57
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Fig. 9. Inverse pole figures of SD and SPN derived from two regions mapped in Fig. 5 for the quasi-static specimen: (a) and (b) for the region A; (c) and (d) for the region B.
(a)
(b)
SPN
SD (d)
(c)
SD
SPN
Fig. 10. Inverse pole figures of SD and SPN derived from outside of ASB mapped in Fig. 6 and ASB mapped in Fig. 7 for the dynamic specimen: (a) and (b) for outside of ASB, (c) and (d) for ASB.
recrystallization.
rotations of the subgrain boundary within the deformation time (~80 μs) at subgrain sizes of 0.5 µm and temperature of 0.5 Tm. In Fig. 11(a) the temperature was varied from 0.4 to 0.7 Tm for a subgrain size of 0.5 µm, and in Fig. 11(b) the subgrain size (L) was varied from 0.25 to 1 µm at 0.5 Tm. Thus, it is reasonable to believe that the reorientation of subgrain boundaries/dynamic recrystallization can take place during the ASB formation. In summary, the equiaxed ultrafine grains observed in this study are the product of dynamic
4. Conclusion This paper documented an analysis of quasi-static (10−3 s−1) and dynamic (104 s−1) forced shear deformation testing of Ti-5Mo-5V-8Cr3Al alloy at room temperature. The major results can be summarized as below: 58
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Fig. 11. Angle of rotation of subgrain boundary in the dynamic specimen as a function of time for (a) different temperatures at subgrain size of 0.5 µm and (b) different subgrain size (0.25, 0.5, 0.75 and 1 µm) at T/Tm=0.5. [9] L.J. Kuang, Z.Y. Chen, Y.H. Jiang, Z.M. Wang, R.K. Wang, C.M. Liu, Adiabatic shear behaviors in rolled and annealed pure titanium subjected to dynamic impact loading, Mater. Sci. Eng. A 685 (2017) 95–106. [10] Z.Z. Li, B.F. Wang, S.T. Zhao, R.Z. Valiev, K.S. Vecchio, M.A. Meyers, Dynamic deformation and failure of ultrafine-grained titanium, Acta Mater. 125 (2017) 210–218. [11] Y.H. Jiang, Z.Y. Chen, C.K. Zhan, T. Chen, R.K. Wang, C.M. Liu, Adiabatic shear localization in pure titanium deformed by dynamic loading: microstructure and microtexture characteristic, Mater. Sci. Eng. A 640 (2015) 436–442. [12] H.Y. Zhan, W.D. Zeng, G. Wang, D. Kent, M. Dargusch, Microstructural characteristics of adiabatic shear localization in a metastable beta titanium alloy deformed at high strain rate and elevated temperatures, Mater. Charact. 102 (2015) 103–113. [13] J. Peirs, W. Tirry, B. Amin-Ahmadi, F. Coghe, P. Verleysen, L. Rabet, D. Schryvers, J. Degrieck, Microstructure of adiabatic shear bands in Ti6Al4V, Mater. Charact. 75 (2013) 79–92. [14] M.A. Meyers, V.F. Nesterenko, J.C. LaSalvia, Q. Xue, Shear localization in dynamic deformation of materials: microstructural evolution and self-organization, Mater. Sci. Eng. A 317 (2001) 204–225. [15] S.J. Pérez-Bergquist, G.R. Gray Ш, E.K. Cerreta, C.P. Trujillo, A. Pérez-Bergquist, The dynamic and quasi-static mechanical response of three aluminum armor alloys: 5059, 5083 and 7039, Mater. Sci. Eng. A 528 (2011) 8733–8741. [16] M.T. Pérez-Prado, J.A. Hines, K.S. Vecchio, Microstructural evolution in adiabatic shear bands in Ta and Ta-W alloys, Acta Mater. 49 (2001) 2905–2917. [17] M.A. Meyers, Y.B. Xu, Q. Xue, M.T. Pérez-Prado, T.R. McNelley, Microstructural evolution in adiabatic shear localization in stainless steel, Acta Mater. 51 (2003) 1307–1325. [18] L.M. Dougherty, E.K. Cerreta, G.T. Gray III, C.P. Trujillo, M.F. Lopez, K.S. Vecchio, G.J. Kusinski, Mechanical behavior and microstructural development of lowcarbon steel and microcomposite steel reinforcement bars deformed under quasistatic and dynamic shear loading, Metall. Mater. Trans. A 40 (2009) 1835–1850. [19] A. Bhattacharyya, G. Ravichandran, D. Rittel, Strain rate effect on the evolution of deformation texture for α-Fe, Metall. Mater. Trans. A 37 (2006) 1137–1145. [20] Y.L. Bai, M.A. Meyers, L.E. Murr (Eds.), Shock Wave and High-Strain-Rate Phenomena in Metals, Plenum Press, New York, 1981. [21] Y. Yang, S.Q. Wu, G.P. Li, Y.L. Li, Y.F. Lu, K. Yang, P. Ge, Evolution of deformation mechanisms of Ti-22.4Nb-0.73Ta-2Zr-1.34O alloy during straining, Acta Mater. 58 (2010) 2778–2787. [22] Q. Xue, G.T. Gray III, B.L. Henrie, S.A. Maloy, S.R. Chen, Influence of shock prestraining on the formation of shear localization in 304 stainless steel, Metall. Mater. Trans. A 36 (2005) 1471–1486. [23] D. Jorge-Badiola, A. Iza-Mendia, I. Gutiérrez, Study by EBSD of the development of the substructure in a hot deformed 304 stainless steel, Mater. Sci. Eng. A 394 (2005) 445–454. [24] J.L. Sun, P.W. Trimby, F.K. Yan, X.Z. Liao, N.R. Tao, J.T. Wang, Shear banding in commercial pure titanium deformed by dynamic compression, Acta Mater. 79 (2014) 47–58. [25] J.A. Hines, K.S. Vecchio, Recrystallization kinetics within adiabatic shear bands, Acta Mater. 45 (1997) 635–649. [26] C.G. Li, J.M. Ma, J. Deng, Titanium and titanium alloys, in: B.Y. Huang, C.G. Li, L.K. Shi, G.Z. Qiu, T.Y. Zuo (Eds.), China Material Engineering Canon, Chemical Industry Press, Beijing, 2006, pp. 644–651. [27] V.F. Nesterenko, M.A. Meyers, J.C. LaSalvia, M.P. Bondar, Y.J. Chen, Y.L. Lukyanov, Shear localization and recrystallization in high-strain, high-strainrate deformation of tantalum, Mater. Sci. Eng. A 229 (1997) 23–41. [28] B.F. Wang, J.Y. Sun, E.N. Hahn, X.Y. Wang, Shear localization and its related microstructure mechanism in a fine-grain-sized near-beta Ti alloy, J. Mater. Eng. Perform. 24 (2015) 477–483.
(1) Compared with the quasi-static deformation, a higher maximum shear stress and a shear instability stage are observed on the dynamic shear stress-shear strain curve due to the strain rate hardening and thermal softening effect, respectively. (2) An adiabatic shear band consisting of ultrafine equiaxed grains is only developed in the dynamic specimen, while a wider shear region is formed in the quasi-static specimen. High microhardness in the shear region of quasi-static specimen and the adiabatic shear band is respectively due to strain hardening and grain refining. (3) Microtexture analysis reveals that a stable orientation, in which the {110} planes and < 111 > directions are respectively parallel to the shear plane and shear direction, develops in both specimens, while the texture of adiabatic shear band is more well-defined than that of shear region in the quasi-static specimen. (4) The thermodynamic calculation reveals that the temperature within the adiabatic shear band is higher than the recrystallization temperature. Based on the rotational dynamic recrystallization mechanism, the kinetic calculations reveal that dynamic recrystallization can occur during the process of adiabatic shear band formation. Acknowledgement This work was supported by the National Natural Science Foundation of China (NSFC) for the financial support (Project 50871125). References [1] Y.B. Xu, J.H. Zhang, Y.L. Bai, M.A. Meyers, Shear localization in dynamic deformation: microstructural evolution, Metall. Mater. Trans. A 39 (2008) 811–843. [2] C. Zener, J.H. Hollomon, Effect of strain rate upon plastic flow of steel, J. Appl. Phys. 15 (1944) 22–32. [3] B. Dodd, Y.L. Bai, Adiabatic Shear Localization: Frontiers and Advances, second ed, Elsevier Science Ltd, London, 2012. [4] P. Longère, A. Dragon, Dynamic vs. quasi-static shear failure of high strength metallic alloys: experimental issues, Mech. Mater. 80 (2015) 203–218. [5] J. Peirs, P. Verleysen, J. Degrieck, F. Coghe, The use of hat-shaped specimens to study the high strain rate shear behaviour of Ti–6Al–4V, Int. J. Impact Eng. 37 (2010) 703–714. [6] E.K. Cerreta, J.F. Bingert, G.T. Gray, C.P. Trujillo, M.F. Lopez, C.A. Bronkhorst, B.L. Hansen, Microstructural examination of quasi-static and dynamic shear in high-purity iron, Int. J. Plast. 40 (2013) 23–38. [7] A.R. Shahan, A.K. Taheri, Adiabatic shear bands in titanium and titanium alloys: a critical review, Mater. Des. 14 (1993) 243–250. [8] Y.B. Xu, Y.L. Bai, M.A. Meyers, Deformation, phase transformation and recrystallization in the shear bands induced by high-strain rate loading in titanium and its alloys, J. Mater. Sci. Technol. 22 (2006) 737–746.
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Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Quasi-static and dynamic forced shear deformation behaviors of Ti-5Mo5V-8Cr-3Al alloy
MARK
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Zhiming Wang, Zhiyong Chen , Congkun Zhan, Lianjun Kuang, Jianbo Shao, Renke Wang, Chuming Liu School of Materials Science and Engineering, Central South University, Changsha 410083, China
A R T I C L E I N F O
A BS T RAC T
Keywords: Ti-5Mo-5V-8Cr-3Al alloy Forced shear deformation Adiabatic shear band Microtexture Hardness
The mechanical behavior and microstructure characteristics of Ti-5Mo-5V-8Cr-3Al alloy were investigated with hat-shaped samples compressed under quasi-static and dynamic loading. Compared with the quasi-static loading, a higher shear stress peak and a shear instability stage were observed during the dynamic shear response. The results showed that an adiabatic shear band consisting of ultrafine equiaxed grains was only developed in the dynamic specimen, while a wider shear region was formed in the quasi-static specimen. The microhardness measurements revealed that shear region in the quasi-static specimen and adiabatic shear band in the dynamic specimen exhibited higher hardness than that of adjacent regions due to the strain hardening and grain refining, respectively. A stable orientation, in which the crystallographic {110} planes and < 111 > directions were respectively parallel to the shear plane and shear direction, developed in both specimens. And the microtexture of the adiabatic shear band was more well-defined than that of the shear region in the quasistatic specimen. Rotational dynamic recrystallization mechanism was suggested to explain the formation of ultrafine equiaxed grains within the adiabatic shear band by thermodynamic and kinetic calculations.
1. Introduction Adiabatic shear band (ASB) is an important deformation mode that intensive deformation localizes in a narrow band when metal deformed under dynamic loading [1]. It is generally recognized that the formation of shear band is a result of the effect of thermal softening exceeding that of strain and strain rate hardening [2,3]. With the formation of the shear band, the bearing capacity of structural material would decrease sharply and even lead to a catastrophic failure because cracks always nucleate and propagate within the ASB [3–5]. Meanwhile, the investigation on quasi-static experiment contributes to a better understanding of the dynamic deformation, and low strain rate deformation is frequently involved during the processing and application of metallic material. Thus, much attention has been paid to exploring the mechanical behavior and microstructure development in various metals and alloys during quasi-static and dynamic deformation. Some experimental and simulation studies [4–6] have revealed that the shear stress is related to the strain rate and the dimensions of hat-shaped specimen. The mechanical curve of hat-shaped specimen deformed under quasi-static loading presents a continuous hardening characteristic, and yet a stress collapse would take place on dynamic shear response. It has been reported that titanium and its alloys are
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Corresponding author. E-mail address: [email protected] (Z. Chen).
http://dx.doi.org/10.1016/j.msea.2017.03.005 Received 21 January 2017; Received in revised form 1 March 2017; Accepted 2 March 2017 Available online 08 March 2017 0921-5093/ © 2017 Elsevier B.V. All rights reserved.
very susceptible to form ASB during dynamic deformation due to their poor thermal conductivity [7,8]. Numerous studies on titanium and its alloys have revealed that the microstructure of ASB consists of ultrafine equiaxed grains, which is a result of dynamic recrystallization [8–13]. Based on this remarkable feature and an extremely short deformation time, a new mechanism named as rotational dynamic recrystallization (RDRX) was proposed by Meyers et al. [14]. It has also been reported that a well-developed shear band would not be formed under the dynamic condition, but the shear localization is more pronounced in the dynamic specimen than that in the quasi-static specimen [15]. Grains adjacent to the ASB represent a special orientation variation that the crystallographic {110} planes and < 111 > directions respectively tend to parallel to the shear plane and shear direction in Ta and Ta-W alloys [16] and stainless steel [17] (body-centered cubic structure metals). Dougherty et al. [18] indicated that the grains within the ASB in steel show three type orientations: {112} < 111 > , {110} < 111 > and {110} < 001 > . These well-defined simple shear texture formed in the dynamic specimen implies that dislocation slip in the {110} and {112} planes along the < 111 > directions. Additionally, Bhattacharyya et al. [19] reported that the deformation texture appears sharper for dynamic specimen compared with quasi-static specimen at large strains ( > 1.0). Thus, the strain rate is an important factor to affect
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3. Results and discussions
the mechanical property, microstructure and microtexture development of metals. Ti-5Mo-5V-8Cr-3Al alloy is a kind of typical metastable beta titanium alloy, which would experience different strain rate deformations during its service lifespan. However, the research on the mechanical response, microstructure and microtexture characteristics of beta titanium alloys deformed under quasi-static and dynamic forced shear conditions is still scanty. In this paper, we investigated the forced shear deformation behaviors of Ti-5Mo-5V-8Cr-3Al alloy under quasi-static and dynamic conditions, and focused on the deformed microstructure and microtexture features. Additionally, the thermodynamic and kinetic calculations were performed to verify the RDRX mechanism. The findings in this work advance our understanding of the force shear deformation behaviors of Ti-5Mo-5V-8Cr-3Al alloy under quasi-static and dynamic loading.
3.1. Shear stress-shear strain curve According to Longère et al. [4], the shear stress (τ) and shear strain (γ) of quasi-static and dynamic forced shear deformation can be calculated by the following equations:
τ=
F Sshear
(1)
γ=
ΔL Wshear
(2)
Sshear =
π D+d D−d 2 ( ) + H2 cos α 2 2
α = arctan
2. Experimental
D−d 2H
(3) (4)
where F is the load applied on the specimen, ΔL is the relative displacement of the top and bottom end. Sshear and Wshear are the section area and width of the shear region, respectively. D and d are top and bottom diameter of the hat-shaped specimen, respectively. α is the angle between shear direction and loading axis. H is the shear region height. The shear stress-shear strain curves of Ti-5Mo-5V-8Cr-3Al alloy during quasi-static deformation at the strain rate of approximately 1.0×10−3 s−1 and dynamic deformation at the strain rate of approximately 6.3×104 s−1 are shown in Fig. 3. The compression displacements (ΔL) in these two tests are the same. Therefore, the shear strain (γ) of the dynamic deformation was larger than that of the quasi-static deformation because the width of the shear region (Wshear) in the dynamic specimen was smaller. The two curves are quite different, except for a similar elastic region. The shear stress of quasi-static sample increased with the increasing strain after the yield point due to the strain hardening, but the rate of strain hardening decreased gradually. The dynamic curve can be divided into three stages as the denoting point (a, b, c, d) in Fig. 3. In the first stage (a-b), the shear stress increased with the increasing shear strain. In the second stage (b-c), the shear stress started to decline with the increasing shear strain. Hence, the shear stress (point b) reached the maximum value of 960 MPa at the shear strain of 0.61. According to the maximum stress criterion for instability deformation [20], the point b represented the onset of unstable deformation, after which the deformation began to localize into an ASB. In the third stage (c-d), the shear stress varied slightly and a “plateau” was formed due to the competing process of the work hardening and the thermal softening introduced by significant rising temperature.
The forged Ti-5Mo-5V-8Cr-3Al alloy plate with dimensions of 200 mm×80 mm×60 mm was kept at the temperature of 1203 K (930 °C) for 55 min, and subsequently the thick sheet was hot-rolled from 60 to 12 mm, yielding a cumulative rolling reduction of 80%. The initial microstructure of hot-rolled Ti-5Mo-5V-8Cr-3Al alloy plate is shown as the 3D view in Fig. 1, where strip grains were observed in the hot-rolled plate. The tested hat-shaped specimens, whose dimensions are shown in Fig. 2(a), were fabricated with loading axis paralleling to the normal direction of the titanium alloy plate. The quasi-static (~10−3 s−1) and dynamic (~104 s−1) forced shear deformation were performed by an Instron apparatus and a SHPB system at room temperature. Specimens for microstructure characterization were cut from the deformed hat-shaped samples along the loading axis by means of electrical discharge machining. The sectioned surfaces for metallographic observation were polished to a mirror finish and then etched with 2 ml HF+15 ml HNO3+83 ml H2O. Vickers microhardness was obtained using an HVS-1000 Microhardness Tester with a load of 50g and a dwell time of 10 s. Specimens for electron backscatter diffraction (EBSD) measurement were prepared by mechanical polishing and electro polishing using a solution of 60 ml HClO4+360 ml CH3(CH2)3OH+600 ml CH3OH on Automatic TwinJet-Electro polishing device at 75 V and −30 °C. EBSD observations of the electrolytic polishing region (Fig. 2(b)) were carried out on a FEI Sirio200 scanning electron microscope system with an acceleration voltage of 20 kV. Microstructure and microtexture were also analyzed by available commercial TSL-OIM Version 5.0 software.
3.2. Microstructure characteristic and microhardness ND
An enlarged optical micrograph of the shear region (Fig. 2) in the quasi-static and dynamic specimen was respectively shown in Fig. 4(a) and (b). As marked in Fig. 4, the left ends were the top ends of the hatshaped samples and the right ends were the corresponding bottom ends. As shown in Fig. 4(a), the plastic deformation of quasi-static specimen mainly occurred in a broad region named as shear localization region. The grains within this region were deformed and elongated toward the shear direction (SD), while those outside the region basically kept the original features. It should be also noted that groups of band structures (denoted by some white arrows) located in some grains. In beta titanium alloys, generally, the thin bands are formed due to the dislocation slip [21]. The shear localization region can be preliminary identified as the region between two black dashed lines and its width was approximately 600 µm. Additionally, the distribution of bands revealed that the inhomogeneous deformation within the shear region. The grains of the bottom end experienced more shear deforma-
TD RD Top end
Bottom end Fig. 1. Microstructure of the initial hot-rolled Ti-5Mo-5V-8Cr-3Al alloy plate. ND, RD and TD respectively stand for the normal direction, rolling direction and transverse direction of the hot-rolled plate.
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(a)
(b) Top end
Shear region
Bottom end
Fig. 2. Schematic illustration of hat-shaped sample and specimen preparation for EBSD in the deformed hat-shaped sample: (a) hat-shaped sample, (b) the region for EBSD observation. SD, SPN and ND respectively stand for the shear direction, shear plane normal and section plane normal.
quasi-static specimen, while the case in the dynamic specimen was inverse, which can be related to the distinct stress states in the two specimens [22]. In order to further understand the forced shear deformation behaviors of Ti-5Mo-5V-8Cr-3Al alloy, microstructure (including grain size, grain morphology and grain orientation) was also characterized by EBSD technique. The orientations of grains were represented by an inverse pole figure color code, in which the red, blue and green respectively represented < 001 > , < 111 > and < 101 > direction. The low angle grain boundaries (LAGBs) with misorientation of 2°– 15° and the high angle grain boundaries (HAGBs) above 15° were represented by white and black lines, respectively. Kernel Average Misorientation (KAM) investigation was used to determine the local values of strain energy with calculation parameter at the fifth nearest neighbor pixels and a maximum misorientation angle of 5°. The black regions in maps were those areas where no orientation data could be acquired by EBSD technique. Fig. 5, with a scanning step size of 4 µm, exhibits the EBSD micrographs of shear localization region adjacent to the top end of the quasi-static specimen. The black regions located in the middle part of IQ map (Fig. 5(a)). It could be obviously seen that grains were deformed to generate groups of parallel band structures, which was similar with the optical microcopy observation (Fig. 5(a)). The KAM map (Fig. 5(b)) clearly shows that the plastic strain mainly occurred in the shear region (indicated by red and yellow color).Fig. 5(c) is an inverse pole figure colored orientation map with respect to the shear plane normal (SPN) to exhibit the deformed microstructure. With the shear deformation, grains in both sides were elongated toward the core of the shear region while the directions were opposite. The shear deformation in the right side was more inhomogeneous than that in the left side. Grains in the left side experienced a certain deformation but kept the original orientation, while the shear deformation in the right side was enough to change grains orientation. Therefore, the variation of grains color was more obvious in the right side. The shear region in Fig. 5(c) can be roughly divided into two regions (marked with A and B) for further analysis of microtexture evolution. In the region A, which was far away from the core of the shear region, the grains were slightly deformed and maintained the original characteristic. In the region B, which was the middle area of the shear region, the grains were severely elongated and fragmentized. Two arrows (L1 and L2) were marked in a strip grain and the corresponding misorientation traces were shown in Fig. 5(d). Along the black arrow, the misorientation between neighboring points in the grain did not exceed 6°, while the point-to-origin misorientation continuously increased with the increasing distance. This can be associated to the formation of geometrically necessary dislocations required to accommodate plastic deformation gradients
Fig. 3. Shear stress-shear strain curves of Ti-5Mo-5V-8Cr-3Al alloy during quasi-static and dynamic deformation. (a) Shear locaalization regiion
Ban nd structures
Bottom ennd
Top end
(b) Ad diabatic shear band Top end
Bottom end B
Fig. 4. Optical micrographs of the shear region in the hat-shaped specimen after: (a) quasi-static loading, (b) dynamic loading.
tion than that of the top end. In the dynamic specimen (Fig. 4(b)), the plastic deformation was highly localized in a narrow band named as ASB. The ASB was straight and its width was approximately 40 µm. The propagated direction of the ASB was the maximum shear stress direction – SD. The microstructure within the ASB was not visible via optical microcopy. Grains adjacent to the ASB were elongated toward the band. Consequently, a certain amount of plastic deformation also took place outside the ASB. The microstructure away from the ASB consisted of original coarse grains with little deformation. Besides, the crack at the bottom end was longer than that at the top end in the 53
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Fig. 5. EBSD micrographs of quasi-static deformation specimen (step size: 4 µm): (a) IQ map; (b) KAM map; (c) IPF colored orientation map with respect to SPN; (d) the misorientation profile measured along lines L1 and L2 in (c); (e) inverse pole figure of SPN showing the variation of crystal orientation along the black arrow in (c).
of LAGBs with grains close to the core of the shear region. Fig. 6, with a scanning step size of 3 µm, shows the microstructure of dynamic specimen. The forced shear deformation mainly localized in the ASB (the black area in Fig. 6(a)) which crossed many grains and subdivided the image into two parts. Meanwhile, the strain of grains outside the ASB was well illustrated in the KAM map (Fig. 6(b)). It could be seen that the plastic strain in the left map was larger than that in the right side. As shown in Fig. 6(c), the grains adjacent of the ASB were elongated toward the SD and fragmented. Based on the distribution of LAGBs and the varying color within grains, the deformation mechanism is dislocation slip. Fig. 6(d) shows the detailed misorientation angles measured in grain A and B (in Fig. 6(c)). The maximum misorientation angle between neighboring points along lines L1 and L2
along the black arrow in the strip grain [23]. In contrast, the misorientation trace along the red arrow changed dramatically when it crossed several high angle grain boundaries. Hence, the strip grain was observed to be fragmented along the red arrow direction as a consequence of deformation mainly concentrated on these HAGBs. Meanwhile, the varying color in the strip grain implied lattice rotations. The crystal orientation corresponding to points 1–10 was respectively labeled as 1–10 in Fig. 5(e). It was easy to find that great changes have taken place in the crystal orientation of the strip grain. As the blue arrow indicated, the crystallographic plane paralleling to shear plane gradually transformed from a {111} plane into a {110} plane. The profuse color variation (or orientation) within grains indicated extensive dislocation slip, which was also indicated by the increasing number 54
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Fig. 6. EBSD micrographs showing the microstructure of dynamic specimen (step size: 3 µm): (a) IQ map, (b) KAM map, (c) IPF colored orientation map, (d) the misorientation profile measured along line L1 and L2 in (c).
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Fig. 7. EBSD micrographs of the adiabatic shear band in the dynamic specimen (step size: 50 nm): (a) IQ map; (b) IPF colored orientation map; (c) the grain size distribution map; (d) the misorientation angle map; (e) enlarged view of an area of (b), black arrows indicate the HAGBs; (f) the misorientation profile measured along line L in (e).
grain size is about 0.25 µm). The misorientation angle map (Fig. 7(d)) shows the distribution of identified grain boundaries angle. In short, Fig. 7(a)-(d) reveal that the microstructure within the ASB consisted of equiaxed ultrafine grains with low dislocation density and well defined high-angle grain boundaries. Besides the equiaxed grains bounded by HAGBs, some elongated large grains were observed in the ASB. Fig. 7(e) gives an enlarged view of an elongated grain (marked by red dotted oval) of Fig. 7(b). This grain was surrounded by HAGBs (black lines) and divided by LAGBs (white lines) inside or among the fragmentized grains. The LAGBs would further evolve into HAGBs
was 1° and 4.5°, and the accumulative misorientation angle was 9° and 18°, respectively. This means the stored energy of grain B is much higher than that of grain A because of grain B is nearer to the shear band. Fig. 7 shows the EBSD micrographs were obtained from the inside of the ASB in the dynamic specimen by high-resolution EBSD scanning (step size: 50 nm). As shown in Fig. 7(a), the microstructure within the ASB was composed of ultrafine equiaxed grains. In Fig. 7(b), most grain colors were blue and green, and a large amount of HAGBs and LAGBs can be seen. Fig. 7(c) shows the grain size distribution (average 56
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Fig. 10 shows the microtexture of the grains in the dynamic specimen. As shown in the IPFs of SD, the intensity around < 001 > direction weakened obviously while the < 111 > component had a pronounced increase. In the IPFs of SPN, the < 001 > component disappeared and the intensity of < 112 > direction decreased, while a concentrating peak arose in the < 101 > direction. It reveals that most of grains within the ASB have their {110} planes and < 111 > directions respectively parallel to the shear plane and shear direction. The microtexture characteristic was in accord with the grains color in Fig. 8(b). Compared with the microtexture development in quasi-static specimen, a well-defined texture formed during the dynamic deformation due to a higher strain occurred in the ASB. Moreover, it could be concluded that the predominant mechanism operating during forced shear deformation in Ti-5Mo-5V-8Cr-3Al alloy specimen is dislocation slip in the {110} planes along the < 111 > directions. Fig. 8. Vickers microhardness of the quasi-static and dynamic specimen.
3.4. Adiabatic temperature rise and dynamic recrystallization with further deformation. Actually, some parts of LAGBs, as indicated by four black arrows in Fig. 7(e), have transformed into HAGBs. The gradual transformation process is regarded as subgrain rotation nucleation stage in continuous recrystallization [24], which results in the high fraction of HAGB in the shear band, as shown in Fig. 7(d). Fig. 7(f) displays the point-to-point and point-to-origin misorientation angle variation along line L in the elongated grain. The point-to-point curve shows that there are three misorientation jumps (indicate the locations of LAGBs) for the pileup of dislocations, which allows the definition of several separated regions within the grain. Fig. 8 shows the average Vickers microhardness of the dynamic and quasi-static specimens. It should be noted that the microhardness values of the two specimens decreased from the middle of shear region to the matrix. The decreasing rate in the dynamic specimen was greater than that in the quasi-static specimen. This indicates that the width of the shear region in quasi-static specimen is much smaller than that in the quasi-static specimen, which is in accord with the above microstructure observations. As reported [11], high microhardness can be attributed to the strain hardening and grain refining. It is worth mentioning that the indentation size was slightly smaller than the width of the ASB to obtain a microhardness of the ASB. And the size of indentation was much smaller than the average grain size in the shear localization region and the outside ASB. Therefore, higher microhardness in the shear localization region and the vicinity of the ASB should be mainly attributed to the strain hardening. The highest microhardness was obtained in the ASB due to the grain refining.
Under the quasi-static condition, the loading time was sufficient to dissipate the heat generated by deformation. While, the heat generated by the localized plastic deformation cannot dissipate during the short dynamic loading duration. Thus, the dynamic deformation process can be regarded as adiabatic in perspective of thermodynamic. And the temperature (T) within ASB can be calculated by the following equation [25]:
T=
β Cνρ
∫0
γ
τ dγ + T0
(5)
where β is the fraction of plastic work converted into heat (assumed to be a constant 0.9 in this case [3]) and T0 is the ambient temperature (298 K). ρ is the mass density (4810 kg/m3), and Cν is heat capacity (542 J/K) of Ti-5Mo-5V-8Cr-3Al alloy [26]. The calculation revealed that the temperature in the shear region of hat-shaped specimen increased with the increasing shear strain. With the increasing temperature, the effect of thermal softening exceeds that of strain and strain rate hardening. Thus, as shown in Fig. 3, a shear instability stage was observed on the dynamic shear stress-shear strain curve. Meanwhile, the theoretically maximum temperature of the ASB can reach ~1330 K which was well above the temperature for dynamic recrystallization of 940 K (~0.5 Tm, Tm is the melting point). Therefore, the equiaxed ultrafine grains with high-angle boundaries observed by EBSD (Fig. 8) should be a product of dynamic recrystallization. Hines et al. [25] pointed out that the traditional dynamic recrystallization mechanisms are excessively slow in kinetic time to account for the formation of recrystallized grains during high-strain-rate deformation. Considering the recrystallization kinetic time, the rotational dynamic recrystallization mechanism proposed by Nesterenko and Meyers [14,27] is reasonable to account for the formation of recrystallization grains within ASB. Hence, the kinetic calculation can be described by the following equation [17,27]:
3.3. Microtexture characteristic It is well accepted that the predominant deformation of hat-shaped samples is shear. Shear textures are conventionally defined in terms of the crystallographic plane {hkl} and direction < uvw > , parallel to the shear plane and shear direction, respectively [6,9,11,16–18]. The microtextures of region A and B in Fig. 5(c) were calculated and illustrated in the inverse pole figures (IPFs) of SD and SPN. In Fig. 9, the IPFs of SD show grains orientation did not undergo obvious change from the original orientations. Thus, the orientation that < 111 > and < 112 > directions parallel to SD has already been stable. On the contrary, the IPFs of SPN show an obvious microtexture variation. The concentrative peak of grain orientation changed from < 111 > to < 101 > direction with the decreasing distance to the core of the shear localization region, and a weak peak around < 112 > was retained. Thus, most of grains in the shear region showed their crystal plane paralleling to the shear plane changes from the {111} planes to the {110} planes during the plastic deformation, and some grains retained their original orientation that the {112} planes parallel to the shear plane. It is consistent with the microtexture evolution of the strip grain in Fig. 5(c).
3 tan θ − 2 cos θ 3 − 6 sin θ
=
−
4 3 9
4δηD exp(−Q / RT ) t LKT
ln
2+ 3 2− 3
+
2 3
+
4 3 9
ln
tan(θ / 2) − 2 − 3 tan(θ / 2) − 2 + 3
(6)
where θ is the rotation angle for subgrain boundaries (0°–30°), L is the average diameter of subgrain, K is the Boltzmann constant, T is the temperature in shear band, t is the time, δ is the grain boundary thickness, η is the grain boundary energy, D is the grain boundary diffusion coefficient, Q is the activation energy of grain boundary diffusion. There is no kinetic parameter of Ti-5Mo-5V-8Cr-3Al alloy currently, so the kinetic parameters of another beta titanium alloy, Ti5Al-5Mo-5V-1Cr-1Fe, are referred [28]: δ=5.8×10−10 m, η=1.19 J/m2, D=2.8×10−5 m2/s, Q=156 kJ/mol, R =8.314 J/(K mol), K=1.38×10−23 J/K. The kinetic calculation results, shown in Fig. 11, predict significant 57
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Fig. 9. Inverse pole figures of SD and SPN derived from two regions mapped in Fig. 5 for the quasi-static specimen: (a) and (b) for the region A; (c) and (d) for the region B.
(a)
(b)
SPN
SD (d)
(c)
SD
SPN
Fig. 10. Inverse pole figures of SD and SPN derived from outside of ASB mapped in Fig. 6 and ASB mapped in Fig. 7 for the dynamic specimen: (a) and (b) for outside of ASB, (c) and (d) for ASB.
recrystallization.
rotations of the subgrain boundary within the deformation time (~80 μs) at subgrain sizes of 0.5 µm and temperature of 0.5 Tm. In Fig. 11(a) the temperature was varied from 0.4 to 0.7 Tm for a subgrain size of 0.5 µm, and in Fig. 11(b) the subgrain size (L) was varied from 0.25 to 1 µm at 0.5 Tm. Thus, it is reasonable to believe that the reorientation of subgrain boundaries/dynamic recrystallization can take place during the ASB formation. In summary, the equiaxed ultrafine grains observed in this study are the product of dynamic
4. Conclusion This paper documented an analysis of quasi-static (10−3 s−1) and dynamic (104 s−1) forced shear deformation testing of Ti-5Mo-5V-8Cr3Al alloy at room temperature. The major results can be summarized as below: 58
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Fig. 11. Angle of rotation of subgrain boundary in the dynamic specimen as a function of time for (a) different temperatures at subgrain size of 0.5 µm and (b) different subgrain size (0.25, 0.5, 0.75 and 1 µm) at T/Tm=0.5. [9] L.J. Kuang, Z.Y. Chen, Y.H. Jiang, Z.M. Wang, R.K. Wang, C.M. Liu, Adiabatic shear behaviors in rolled and annealed pure titanium subjected to dynamic impact loading, Mater. Sci. Eng. A 685 (2017) 95–106. [10] Z.Z. Li, B.F. Wang, S.T. Zhao, R.Z. Valiev, K.S. Vecchio, M.A. Meyers, Dynamic deformation and failure of ultrafine-grained titanium, Acta Mater. 125 (2017) 210–218. [11] Y.H. Jiang, Z.Y. Chen, C.K. Zhan, T. Chen, R.K. Wang, C.M. Liu, Adiabatic shear localization in pure titanium deformed by dynamic loading: microstructure and microtexture characteristic, Mater. Sci. Eng. A 640 (2015) 436–442. [12] H.Y. Zhan, W.D. Zeng, G. Wang, D. Kent, M. Dargusch, Microstructural characteristics of adiabatic shear localization in a metastable beta titanium alloy deformed at high strain rate and elevated temperatures, Mater. Charact. 102 (2015) 103–113. [13] J. Peirs, W. Tirry, B. Amin-Ahmadi, F. Coghe, P. Verleysen, L. Rabet, D. Schryvers, J. Degrieck, Microstructure of adiabatic shear bands in Ti6Al4V, Mater. Charact. 75 (2013) 79–92. [14] M.A. Meyers, V.F. Nesterenko, J.C. LaSalvia, Q. Xue, Shear localization in dynamic deformation of materials: microstructural evolution and self-organization, Mater. Sci. Eng. A 317 (2001) 204–225. [15] S.J. Pérez-Bergquist, G.R. Gray Ш, E.K. Cerreta, C.P. Trujillo, A. Pérez-Bergquist, The dynamic and quasi-static mechanical response of three aluminum armor alloys: 5059, 5083 and 7039, Mater. Sci. Eng. A 528 (2011) 8733–8741. [16] M.T. Pérez-Prado, J.A. Hines, K.S. Vecchio, Microstructural evolution in adiabatic shear bands in Ta and Ta-W alloys, Acta Mater. 49 (2001) 2905–2917. [17] M.A. Meyers, Y.B. Xu, Q. Xue, M.T. Pérez-Prado, T.R. McNelley, Microstructural evolution in adiabatic shear localization in stainless steel, Acta Mater. 51 (2003) 1307–1325. [18] L.M. Dougherty, E.K. Cerreta, G.T. Gray III, C.P. Trujillo, M.F. Lopez, K.S. Vecchio, G.J. Kusinski, Mechanical behavior and microstructural development of lowcarbon steel and microcomposite steel reinforcement bars deformed under quasistatic and dynamic shear loading, Metall. Mater. Trans. A 40 (2009) 1835–1850. [19] A. Bhattacharyya, G. Ravichandran, D. Rittel, Strain rate effect on the evolution of deformation texture for α-Fe, Metall. Mater. Trans. A 37 (2006) 1137–1145. [20] Y.L. Bai, M.A. Meyers, L.E. Murr (Eds.), Shock Wave and High-Strain-Rate Phenomena in Metals, Plenum Press, New York, 1981. [21] Y. Yang, S.Q. Wu, G.P. Li, Y.L. Li, Y.F. Lu, K. Yang, P. Ge, Evolution of deformation mechanisms of Ti-22.4Nb-0.73Ta-2Zr-1.34O alloy during straining, Acta Mater. 58 (2010) 2778–2787. [22] Q. Xue, G.T. Gray III, B.L. Henrie, S.A. Maloy, S.R. Chen, Influence of shock prestraining on the formation of shear localization in 304 stainless steel, Metall. Mater. Trans. A 36 (2005) 1471–1486. [23] D. Jorge-Badiola, A. Iza-Mendia, I. Gutiérrez, Study by EBSD of the development of the substructure in a hot deformed 304 stainless steel, Mater. Sci. Eng. A 394 (2005) 445–454. [24] J.L. Sun, P.W. Trimby, F.K. Yan, X.Z. Liao, N.R. Tao, J.T. Wang, Shear banding in commercial pure titanium deformed by dynamic compression, Acta Mater. 79 (2014) 47–58. [25] J.A. Hines, K.S. Vecchio, Recrystallization kinetics within adiabatic shear bands, Acta Mater. 45 (1997) 635–649. [26] C.G. Li, J.M. Ma, J. Deng, Titanium and titanium alloys, in: B.Y. Huang, C.G. Li, L.K. Shi, G.Z. Qiu, T.Y. Zuo (Eds.), China Material Engineering Canon, Chemical Industry Press, Beijing, 2006, pp. 644–651. [27] V.F. Nesterenko, M.A. Meyers, J.C. LaSalvia, M.P. Bondar, Y.J. Chen, Y.L. Lukyanov, Shear localization and recrystallization in high-strain, high-strainrate deformation of tantalum, Mater. Sci. Eng. A 229 (1997) 23–41. [28] B.F. Wang, J.Y. Sun, E.N. Hahn, X.Y. Wang, Shear localization and its related microstructure mechanism in a fine-grain-sized near-beta Ti alloy, J. Mater. Eng. Perform. 24 (2015) 477–483.
(1) Compared with the quasi-static deformation, a higher maximum shear stress and a shear instability stage are observed on the dynamic shear stress-shear strain curve due to the strain rate hardening and thermal softening effect, respectively. (2) An adiabatic shear band consisting of ultrafine equiaxed grains is only developed in the dynamic specimen, while a wider shear region is formed in the quasi-static specimen. High microhardness in the shear region of quasi-static specimen and the adiabatic shear band is respectively due to strain hardening and grain refining. (3) Microtexture analysis reveals that a stable orientation, in which the {110} planes and < 111 > directions are respectively parallel to the shear plane and shear direction, develops in both specimens, while the texture of adiabatic shear band is more well-defined than that of shear region in the quasi-static specimen. (4) The thermodynamic calculation reveals that the temperature within the adiabatic shear band is higher than the recrystallization temperature. Based on the rotational dynamic recrystallization mechanism, the kinetic calculations reveal that dynamic recrystallization can occur during the process of adiabatic shear band formation. Acknowledgement This work was supported by the National Natural Science Foundation of China (NSFC) for the financial support (Project 50871125). References [1] Y.B. Xu, J.H. Zhang, Y.L. Bai, M.A. Meyers, Shear localization in dynamic deformation: microstructural evolution, Metall. Mater. Trans. A 39 (2008) 811–843. [2] C. Zener, J.H. Hollomon, Effect of strain rate upon plastic flow of steel, J. Appl. Phys. 15 (1944) 22–32. [3] B. Dodd, Y.L. Bai, Adiabatic Shear Localization: Frontiers and Advances, second ed, Elsevier Science Ltd, London, 2012. [4] P. Longère, A. Dragon, Dynamic vs. quasi-static shear failure of high strength metallic alloys: experimental issues, Mech. Mater. 80 (2015) 203–218. [5] J. Peirs, P. Verleysen, J. Degrieck, F. Coghe, The use of hat-shaped specimens to study the high strain rate shear behaviour of Ti–6Al–4V, Int. J. Impact Eng. 37 (2010) 703–714. [6] E.K. Cerreta, J.F. Bingert, G.T. Gray, C.P. Trujillo, M.F. Lopez, C.A. Bronkhorst, B.L. Hansen, Microstructural examination of quasi-static and dynamic shear in high-purity iron, Int. J. Plast. 40 (2013) 23–38. [7] A.R. Shahan, A.K. Taheri, Adiabatic shear bands in titanium and titanium alloys: a critical review, Mater. Des. 14 (1993) 243–250. [8] Y.B. Xu, Y.L. Bai, M.A. Meyers, Deformation, phase transformation and recrystallization in the shear bands induced by high-strain rate loading in titanium and its alloys, J. Mater. Sci. Technol. 22 (2006) 737–746.
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