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Adiabatic shear behaviors in rolled and annealed pure titanium subjected to dynamic impact loading
Materials Science & Engineering A 685 (2017) 95–106
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Adiabatic shear behaviors in rolled and annealed pure titanium subjected to dynamic impact loading
MARK
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Lianjun Kuang, Zhiyong Chen , Yanghui Jiang, Zhiming Wang, 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: Shear bands Titanium Microstructure Twinning Dynamic recrystallization
The hat-shaped samples cut from rolled and annealed titanium plates were prepared to explore the adiabatic shear behaviors subjected to high-strain-rate deformation operated via Split Hopkinson Pressure Bar. The dynamic shear response calculation reveals that dynamic deformation processes of both state samples can be divided in similar three stages but rolled sample shows a higher susceptibility of adiabatic shear localization compared with the annealed one. Optical microscopy and electronic backscatter diffraction technique (EBSD) were used to systematically analyze the microstructure and texture characteristics. The results show that adiabatic shear bands form in both state samples and rotational dynamic recrystallization (RDRX) occurs within shear area and results in the formation of ultrafine equiaxed grains. Furthermore, ultrafine equiaxed grains within adiabatic shear bands have the same texture feature that < 11–20 > direction and {10-10} plane parallel to macro local shear direction and shear plane respectively. In the deformation region around the shear band, {10–12} < –1011 > tensile and {11–22} < 11-2-3 > compressive two types twins are observed in both state samples and {10–12} < –1011 > tensile twins are more frequently observed in rolled sample. In the rolled sample, {10–12} < –1011 > tensile twins are more likely to happen in the hat-brim side than the hat-body side due to the difference of stress state in two sides.
1. Introduction Shear localization is a common phenomenon for metallic materials under high-strain-rate deformation such as penetration and it always goes with the formation of shear band. Shear localization can be regarded as adiabatic process because the heat within the narrow shear band area is hard to diffuse in extremely short time [1]. Thus, this process is also called adiabatic shear localization. Besides, adiabatic shear localization is one of the important failure mechanisms of materials under high-strain-rate deformation, which makes it closely related to the service life limit of material [2]. Therefore, numerous studies have been conducted on adiabatic shear localization of various metals and alloys, including steel, magnesium, titanium, copper, aluminum and so on [3–9]. And, in particular, the advantages of titanium and its alloys make them popular in various industries: medical applications (for the excellent biocompatibility), offshore applications (for the superior corrosion resistance), military and aerospace applications (for the high specific strength) and sports equipment, etc. [10]. As titanium and its alloys used in military and aerospace usually suffer extreme conditions such as high speed impact, adiabatic shear localization contributes to the failure of materials a lot.
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And it is easy to form adiabatic shear band in titanium and its alloys under dynamic loading because of their low thermal conductivity [11,12]. Hence, adiabatic shearing behaviors of titanium and its alloys, including microstructural evolution and theoretical explanation, have been extensively investigated by simulation research and experimental study during recent decades [13–18]. Zherebtsov et al. and Yang et al. reported that, in deformed titanium, there are ultrafine nano-size grains within the adiabatic shear band after dynamic loading [19,20]. Besides, Chichili et al. investigated microstructure in annealed polycrystalline titanium subjected to dynamic deformation and Meyers et al. proposed rotational dynamic recrystallization (RDRX) theory based on the nano-size equiaxed grains with low density of dislocations within adiabatic shear band [21,22]. In addition, Rittel et al. reported that dynamic recrystallization (DRX) not only precedes adiabatic shear failure but it is also likely to be a dominant micromechanical factor in the very generation of the band [23]. Nevertheless, the differences of microstructural evolution processes between deformed and annealed original structure of identical component titanium have not been systematically studied. Sun et al. suggested that deformation stored energy has significant effects on the final average grain size in the
Corresponding author. E-mail address: [email protected] (Z. Chen).
http://dx.doi.org/10.1016/j.msea.2017.01.011 Received 8 December 2016; Received in revised form 28 December 2016; Accepted 3 January 2017 Available online 04 January 2017 0921-5093/ © 2017 Elsevier B.V. All rights reserved.
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solution of 4 ml hydrofluoric acid +20 ml nitric acid +200 ml distilled water. Samples for EBSD, cutting at the maximum diameter of the hap-shape, were primarily mechanical grinded by using different grit papers with particle sizes from 400 to 2000 mesh, then electrolytic polished on a twin-jet polisher in a solution of 10 ml perchloric acid +70 ml n-Butyl alcohol +120 ml methanol at 90 V and −20 °C for 90 s. The SEM picture of twin-jet samples for EBSD is illustrated in Fig. 1(c). EBSD studies were carried out on a FEI Helios Nanolab 600i scanning electron microscope equipped with an orientation imaging microscopy software developed by HKL system. High resolution EBSD measurements were obtained using a step size of 120 nm while the macro area scans used a step size of 2 µm. Channel 5 software was used for microstructure and microtexture analyses based on EBSD data. The misorientations of grain boundaries, which are greater than 15°, are defined as high-angle grain boundaries (HAGBs) in this study while those in the range of 2–15° are defined as low-angle grain boundaries (LAGBs).
adiabatic shear band, which indicated that deformation stored energy in rolled titanium takes some significant effects on microstructure after dynamic deformation [24]. Moreover, Yang et al. reported that the early stage of shear localization involves the formation and multiplication of mechanical twins, giving rise to the twin/matrix lamellar structure aligned along the shear direction [25]. However, the studies focusing on microstructure and microtexture characteristics of adiabatic shear band in deformed titanium with elongating grains and annealed titanium with equiaxed grains are still relatively scanty. The aim of the present work is to perform macroscopic and microscopic investigations of the shear bands and surrounding deformation areas in both rolled and annealed titanium hat-shaped samples via optical microscopy (OM) and electron backscatter diffraction (EBSD) technique. This makes it possible to compare the differences of dynamic behaviors between the two state titanium samples. Specifically, most of the efforts have been focused on the dynamic stress-strain responses, macroscopic morphology of shear bands, microstructure with shear bands and twinning in the surrounding deformation areas. It is worth to be noted that the current study investigates the texture characteristics of shear bands in rolled and annealed titanium of identical component, which are rarely reported in the past researches. Besides, the distinctions of twinning behaviors in different surrounding deformation areas are discussed in this study. This research advances our understanding on adiabatic shear behaviors in different original state titanium and enhances the comprehending of microstructural deformation mechanism.
3. Results and discussions 3.1. Shear stress-shear strain response Since the hat-shaped samples were experimented by a Split Hopkinson Pressure Bar, the shear stress and shear strain in the shear area could be calculated from the data collected by the strain gauge recordings on the incident bar and transmitter bar. The calculation equations were provided by Andrade et al. [26] and displayed as the followings:
2. Experimental
E 0A ε t (t) ⎧ τ= ⎛ d s+ d ⎞ ⎪ π h⎜ 1 2 ⎟ ⎪ ⎝ 2 ⎠ ⎪ ⎨ 2 C0 ∫ t[εi(t) − εt(t)]dt 0 ⎪ γ= w ⎪ 2C 0[ε i(t) − ε t (t)] ⎪ γ̇= ⎩ w
A forged commercially pure α titanium block with the size of 200 mm×80 mm×60 mm was preheated for 50 min at 1103 K, then were rolled to 12 mm in the thickness direction via 7 paths. The final cumulative reduction reached 80%. Then the hot-rolled plate was cut into two pieces, one was placed for the following cutting process and the other was annealed at 1023 K for 120 min in the vacuum furnace after the rolling. Hat-shaped samples (as illustrated in Fig. 1(a)) used in this study were cut from the former rolled plate and the annealed plate, respectively. Both rolled and annealed samples were cut along the normal direction of the titanium plate for the subsequent high-ratestrain deformation. In this step, three same samples were prepared for each state and later tests or investigations are applied to all the samples to avoid accidental errors. Dynamic tests were carried out using a Split Hopkinson Pressure Bar (SHPB) at room temperature. Samples for microstructure characterization were cut from the dynamically deformed hat-shaped samples along the loading axis by wire-electrode cutting (as illustrated in Fig. 1(b)). Metallographic specimens were prepared by standard mechanical polishing and then etched in a
(1)
The shear stress-shear strain curves of rolled and annealed samples obtained from the former equations, shown in Fig. 2, indicate similar stages of dynamic responses with obvious differences in each stage. In this graph, a1, b1, c1 are the points on the rolled state curve and a2, b2, c2, d2 are the points on the annealed state curve. Both the dynamic deformation processes can be divided into three stages: strain hardening stage (0~a1, 0~a2), shearing instability stage (a1~b1, a2~b2), dynamic equilibrium stage (b1~c1, b2~c2). In the first stage, the shapes of two state curves are similar to each other, which indicates that deformation modes of titanium in the strain hardening stage of two state samples are the same to some extent. Here, shear stress increases with the increasing of shear strain from
Fig. 1. Schematic map of hat-shaped sample and EBSD sample: (a) schematic diagram of hat-shaped sample for dynamic loading; (b) schematic diagram of samples cut along the loading axis direction; (c) SEM picture of twin-jet sample for EBSD experiment.
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dissipation energy (ASDE) proposed by Grady [27]. The formation and expansion of adiabatic shear band need to overcome an energy barrier. And the higher for the barrier, the harder for the formation of adiabatic shear band, namely the adiabatic shear sensitivity is weaker. The value of ASDE can be calculated in the following equation: 1
⎛ ⎞4 ρ c 9ρ3cλ3 Γ= ⎜⎜ 3 2 ⎟⎟ α ⎝ τ γα γ̇ ⎠
(2)
In the above equation, Γ represents ASDE, ρ is material's density, c is the specific heat capacity of material, λ is thermal diffusivity which reflects the heat dissipation ability, α is thermal softening coefficient, γ̇ is strain velocity, τγ is the flow stress at γ̇ velocity. Among them, ρ, c, λ and α describe inherent properties of materials, so they keep to be constants regardless of the initial state for a same material at a same loading condition. But flow stress of different initial state samples shows quite different value. Annealed sample get a relatively lower flow stress just before the collapse, therefore its ASDE is much higher than the rolled one. In addition, due to the lack of deformation stored energy, annealed sample needs longer time to deform for energy storing. Meanwhile, the softening effect caused by deformation heat can counteract work-hardening at that stress value, so there is a slowly stress decreasing stage before collapse in annealed curve.
Fig. 2. True stress-strain curves of rolled and annealed samples obtained from Hopkinson tests.
0 to approximate 1.2 until achieving the peak stress. The corresponding strain of the peak point is where the plastic instability stage appears. In the next stage, shear stress decreases sharply with the increasing of shear strain which called stress collapse. The emergence of stress collapse is mainly caused by the dominant status of thermodynamic softening in the competition with work-hardening. Adiabatic shear band starts to form in this stage. In the final dynamic equilibrium stage, thermal softening effect induced by the working heat is equal to hardening effect induced by the deformation, which results in a platform at about 430 MPa shown in the curves for both rolled and annealed samples. And it is interested that the values of the platform in two state curves are almost the same in spite of the differences in the former two stages. However, there are obvious differences in each stage between rolled and annealed samples. At the end of first stage, the rolled sample curve reaches higher top flow stress of about 1150 MPa while the peak flow shear stress of annealed sample is only about 1000 MPa, which could be the result of work-hardening effect. In the second stage, the stress collapse of the rolled sample happened at higher stress and the magnitude of the collapse is greater as well, which indicates that the rolled sample shows higher adiabatic shear sensitivity. Stored energy has important effects on the dynamic loading process [24]. Stored energy in the rolled sample releases while stress collapsing, therefore the formation of adiabatic shear band could be easier because of the energy supplement. Besides, we discover that there is a slowly stress decreasing stage (a2~d2) before shear instability in the annealed curve (as shown in the Fig. 2). The appearance of this stage is related to the initial structure. This phenomenon can be explained using the adiabatic shear
3.2. Macroscopic characteristics 3.2.1. The whole morphology The original structure of annealed sample contains equiaxed grains with an average grain size about 24 µm while the original structure of rolled sample consists of elongated grains (as illustrated in Fig. 3). And the structures of both state samples after dynamic impact have changed especially in the area where forced shear stress concentrates. Fig. 4(a) and (b) illustrate the whole view of adiabatic shear bands and their adjacent areas of rolled and annealed samples via optical microscope. The location of adiabatic shear band in the hat-shaped sample is shown in Fig. 1(b). Adiabatic shear bands form in both state samples and contain significant different structure compared with the adjacent areas. The widths of the shear bands in the two state samples gradually narrow down along the shear direction from the top to the bottom. The widest area can reach around 50 µm while the narrowest area is only about 20 µm. For the adjacent area, structure in the rolled sample inherits rolling feature with lamellar structure and the anneal one still consists of coarse grains. This phenomenon indicates the dramatical shear localization in the shear area. Cracks take place in the two state samples and occur in the ends of adiabatic shear band prior to the adjacent deformation areas. And in every single shear band, crack in the bottom extends more deeply in the shear band along the shear direction while crack in the top extends just a little in the shear band.
Fig. 3. Structures of rolled and annealed plates via optical microscopy: (a) rolled sample; (b) annealed sample.
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contain adiabatic shear bands and the surrounding areas (scanning pace 0.5 µm). We can divide them into two zones due to the grains’ orientation and morphology: adiabatic shear band and surrounding deformation area. The approximate boundaries of these two zones are indicated in white dotted line in Fig. 5. Adiabatic shear bands in both state samples are all filled up with ultrafine grains and need more detailed scanning. The surrounding deformation areas in two sides of the shear band are quite different. In rolled sample, the angle between elongating direction of right side grains and shear direction is quite different from the other side. In annealed sample, grains in the left side are elongated along shear direction apparently while grains in the right side still have some features of equiaxed grains (such as trigeminal grain boundaries). Herein, twins (indicated via black arrows in Fig. 5) in both states are quite clearer than them in Fig. 4 and twins in the surrounding deformation area of rolled sample are observed. Twins observed in Figs. 4 and 5 demonstrate that twinning plays a great role in the deformation of the surrounding deformation areas during dynamic loading. And twinning behavior is deep discussed in the later Section 3.4.
Fig. 4. The whole view of shear band in two state samples via optical microscopy: (a) the shear band in rolled sample; (b) the shear band in annealed sample.
Besides, the shape of the crack in the rolled sample is approximate a straight line while the crack in the annealed sample is serrated. It should be noted that there are apparent twins (some of them are indicated via black arrows in Fig. 4(b)) in the adjacent area of annealed sample and it need more detailed investigating method to affirm whether there are twins in adjacent area of rolled sample.
3.3. Adiabatic shear band 3.3.1. Microstructure characteristics The adiabatic shear band microstructure of rolled and annealed samples are shown in Fig. 6(a) and (b) respectively. Shear bands in both state samples are filled up with ultrafine grains with several LAGBs in the grains. The range of grain sizes within shear band of annealed and rolled states are both about 0.1–1 µm. The formation of the ultrafine grains in the shear band is caused by the heavy deformation and recrystallization. Meanwhile, as we all know that shear band area suffers much higher strain than its surrounding area during dynamic process, which results in significant temperature rise and induces grain coarsening. The range of the grain size is the
3.2.2. The fractional morphology We use EBSD data to represent the grain orientation relationship for the fractional morphology and further analyses in this study. All orientation maps presented in this paper use the inverse pole figure coloring mode at the corner of the Fig. 5, in which the red, blue and green color represents < 0001 > , < 10-10 > and < 11–20 > direction, respectively. HAGBs and LAGBs are indicated by black lines and white lines, respectively. Fig. 5 shows the EBSD maps of rolled and annealed samples, which
Fig. 5. Macroscope EBSD maps of shear band and surrounding area in rolled sample and annealed sample: (a) rolled sample; (b) annealed sample. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
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Fig. 6. Microstructure of adiabatic shear bands in both state samples: (a) shear band in rolled sample; (b) shear band in annealed sample; (c) amplification of elongated grain within the rectangle area in rolled sample; (d) amplification of elongated grain within the rectangle area in annealed sample; (e) misorientations distribution map point to point along the green line in the elongated grain in (c). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
represent shear direction, normal direction and normal direction of shear plane, respectively. The pole figures suggest that grains in the adiabatic shear band have the similar texture characteristic in spite of the different initial microstructure in the shear area. The final orientation of the grains in the adiabatic shear band can be described as followings: the < 11–20 > direction and the {10-10} plane of the grains tend to parallel with the macro local shear direction and shear plane respectively.
outcome of grain refinement and coarsening. Although most of the ultrafine grains are equiaxed, some elongated fine grains are investigated in the shear bands. Fig. 6(c) and (d) represents the elongating grains within the rectangle area in Fig. 6(a) and (b), respectively. And Fig. 6(e) illustrates the misorientation along the green line in the elongating grain shown in Fig. 6(c). The five peaks in the diagram are in correspondence with the five LAGBs along the green line within the grain. This grain is surrounded by fragmentized small grains and irregularly divided into subgrains or substructures of various sizes by the LAGBs inside the grains. The peaks and misorientations of other values reveal the inhomogeneous deformation inside the grain during dynamic loading and formation of deformation cell structures. In Fig. 6(d), subgrain boundaries composed of LAGBs and HAGBs are found in the rectangle area named A and B, which reveals that the HAGBs in the elongated grain are grown from LAGBs and finally lead the subgrains growing into fragmentized fine grains like the surrounding area. Except the microstructure, texture of shear bands is also measured by the detailed EBSD scanning. The pole figures of these two state samples are illustrated in Fig. 7(a) and (b). The SD, ND and SPN
3.3.2. Temperature rising within the ASB Shear localization can be regarded as adiabatic process because the heat within the narrow shear band area is hard to diffuse in extremely short time. The microstructural evolution associated with the dynamic deformation is greatly influenced by the temperature rising during the adiabatic shear banding. And the temperature can be calculated by the following equation [28]:
T=
99
β C vρ
γ
∫ 0
τdγ +T0 (3)
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Fig. 7. The {0001}, {11–20} and {10-10} pole figures in shear band zone and the extracted 3D orientation diagrams of (a) rolled sample; (b) annealed sample.
Fig. 8. Temperature rising curve with stress-strain response curve of two state samples within the shear band: (a) rolled sample; (b) annealed sample.
where, β is the heat-converting factor (0.9) that represents the fraction of plastic energy converting to heat, ρ is the mass density of titanium (4510 kg/m3), Cv is the heat capacity (523 J/K), T0 is the room temperature (298 K), γ is the flow stress and τ is the flow strain, respectively. Temperature rising curves of two state samples are illustrated in Fig. 8 by substituting the dynamic response data during forced plastic deformation into Eq. (3). In both state samples, temperature increases with the increasing of strain. And temperature increases fast at first then increases relatively slowly and increases with an approximately constant velocity till the end. And the temperature in shear band area of rolled sample reaches ~700 K (equal to ~0.36Tm) at shear strain ~1.1 where shear instability occurs (point a1 shown in Fig. 8(a)) while the annealed reaches ~900 K (equal to ~0.46Tm) when the shear strain increase to ~1.8 where shear instability occurs (point a2 shown in Fig. 8(b)). These calculating results indicate that the temperature in the adiabatic shear band area meets the needs of recrystallization of
titanium. And in the subsequent cooling procedure, it only takes several microseconds (μs) to cool to room temperature according to the estimation by using the classical Fourier heat conduction equation [29]. Therefore, after the dynamic deformation, the microstructure in the adiabatic shear band formed at high temperature can be preserved. 3.3.3. Grain refinement mechanism Adiabatic environment and extremely short time are the two important features in shear banding, which makes the dynamic recrystallization (DRX) here quite different from the traditional DRX process. Early in 1997, it was reported by Hines et al. [28] that the DRX happened in shear band was essentially different from the classical DRX especially for the process of high-angle boundary migration and subgrain coalescence which would take a much more time to accomplish. The most accepted recrystallization mechanism in the adiabatic shear band, rotational dynamic recrystallization (RDRX), was presented by Meyers et al. [22,30]. According to RDRX 100
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where, θ is the rotation angle for subgrain boundaries (0–30°); L is the size of the subgrain; k (equal to 1.38×10–23 J/K) is the Boltzmann constant; T is the temperature in the shear band; t is the time for the rotation of subgrain; δDGB is the grain boundary diffusion coefficient and it was experimentally measured by Herzig et al. [31]:
⎡ -153kJmole-1 ⎤ ⎥(m2/s) δDGB=9.2 ×10-14exp⎢ RT ⎣ ⎦
(5)
γb is the grain boundary energy as a function of misorientation that can be calculated by the Read-Shockley equation [32]:
γb=
mechanism, the grains in the adiabatic shear band area experience grain elongating, grain breaking-up and subgrain rotation and the kinetic condition can be described as following equation [30]:
LkT
t=
(6)
where, G (=440 GPa) is shear modulus; b (=0.295 nm) is the module of Burgers vector; α=4; ν=0.33; θ is the misorientation angle between two adjoining lattices which always considered as 15°. The results of Eq. (4) (as shown in the Fig. 9) illustrate the time that subgrains of five different sizes (L=0.1 µm, 0.3 µm, 0.5 µm, 0.8 µm and 1.0 µm) rotate from 0 to 30° needs at 900 K (0.46Tm). Although, in rolled sample, the temperature at plastic instability has not reached 900 K, the temperature increases to more than 900 K rapidly in the subsequent deformation. It is found that the rotation of sub boundaries by an angle of 30° can be accomplished within deformation time (80 μs) when the sizes of the subgrains is less than 1 µm. The grains size within adiabatic shear band in this study is from 0.1 to 1 µm and the temperature in the shear band area is more than 900 K. Therefore, it's reasonable to believe that, in kinetic,
Fig. 9. Angle of rotation of subgrain boundary in titanium as a function of time for different subgrain sizes (L=0.1 µm, 0.3 µm, 0.5 µm, 0.8 µm and 1.0 µm) at 0.46Tm.
4 δDGBγb
Gb θ[1 +ln(α/2 π)-lnθ] 4 π(1 - ν)
3tanθ- 2cosθ 4 3 2 + 3 2 4 3 tan(θ/2)- 2 - 3 ln + + ln 3 - 6sinθ 9 9 tan(θ/2)- 2 + 3 2- 3 3 (4)
Fig. 10. Presentation of elongation of grains in hat-body side and tilting in hat-brim side: (a) the angle between elongating direction of grains and shear direction in initial rolled sample; (b) the angle between elongating direction of grains and shear direction in hat-body side of rolled sample; (c) the whole cross section picture of rolled sample; (d) the whole cross section picture of annealed sample.
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Fig. 11. Tensile twins and compressive twins in rolled and annealed samples: (a) tensile twin in rolled sample; (b) compressive twin in rolled sample; (c) misorientations distribution along line L1; (d) misorientations distribution along line L2; (e) tensile twin in annealed sample; (f) compressive twin in annealed sample; (g) misorientations distribution along line L3; (h) misorientations distribution along line L4.
3.4. Surrounding deformation area characteristics
the occurrence of the RDRX mechanism within the ASB is possible. In summary, the calculation in thermodynamic and kinetic reveals that the rotational dynamic recrystallization can occur theoretically and the observation by EBSD method demonstrates that RDRX actually happens in the adiabatic shear band area.
3.4.1. Morphology features The left side surrounding deformation area in EBSD maps shown in Fig. 5 represents hat-body area (as shown in Fig. 1(a) and (b)) in the 102
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Fig. 12. Tensile twins and compressive twins in two sides of the shear band in annealed sample: (a), (b) for the IPF and IQ map of left side; (c), (d) for the IPF and IQ map of right side. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
because of the compression from the hat-body. In summary, deformations of left and right side surrounding deformation areas are quite different in both state samples. But the diversities of two sides surrounding deformation area show some similar features to some extent. Besides, the stress state of hat-brim and hat-body areas are no more simple shear because of the geometrical changing of hat-shaped samples during dynamic loading.
original hat-shape samples and the other side represents hat-brim area. The grains in hat-body area in both state samples are all elongated along the shear direction. It's much more obvious in the annealed sample. However, it needs further analyses for rolled sample although the grains are typical elongating structure. Because the elongating direction of grains in original rolled sample is vertical to normal direction of the plate, which causes that grains have a certain angle to the shear direction in the initial structure before dynamic loading (as shown in Fig. 10(a)). To ensure that whether the grains tilt to shear direction or not, we measure the angle between elongating direction of hat-body grains and the shear direction in the hat-shaped sample after dynamic loading in Fig. 10(b). The angle decreases to 40° even less in the area near shear band while the angle still maintains at about 58° in the zone far away from shear band (about 100 µm far away from shear band). Due to the above analyses, we can affirm that hat-body grains just near the shear band in both state samples have the tendency tilting to shear direction. In addition, the features of grains in hat-brim area are quite different from the hat-body area. This phenomenon is caused by the changing of geometric conditions during the dynamic deformation. Fig. 10(c) and (d) show the whole cross section of the hat-shape samples, (c) represents rolled sample, (d) represents annealed sample. The geometries of hat-shaped samples have changed a lot after dynamic loading, especially the hat-brim parts. We can find that hatbrim rotates towards the outside due to compression of hat-body in Fig. 10(c). That is why the angle between grains elongating direction and shear direction increases to almost 90° in hat-brim area. Besides, hat-brim suffers compression from hat-body to outside. In this case, Hat-brim suffers not only shear stress but also the compressive stress
3.4.2. Twinning behavior Appearance of twins in both state samples indicates that twinning plays a great role in the dynamic deformation. The analysis on the categories of twins is based on misorientation relationship obtained from EBSD data. Fig. 11(a)-(d) illustrate the tensile and compressive twins in rolled sample and misorientations distributions along L1 and L2 while (e)-(h) illustrate twins and misorientations distributions in annealed sample. Fig. 11(a) and (c) indicate {10–12} < –1011 > tensile twin corresponding to 85° < 11–20 > boundaries and Fig. 11(b) and (d) indicate {11–22} < 11-2-3 > compressive twin corresponding to 64.4° < 10-10 > boundaries in rolled sample. Fig. 11(e)-(h) indicate the same tensile and compressive twins in annealed sample as well. These two types of twins are most frequently observed in this study. Fig. 12 illustrates the twins under different background colors (IQ color and IPF color) in annealed sample including left and right side surrounding deformation areas. Red lines represent tensile twins ({10–12} < –1011 > tensile twin) and blue lines represent compressive twins ({11–22} < 11-2-3 > compressive twin). It can be found that both tensile and compressive twinning have been activated 103
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Fig. 13. Tensile and compressive twin distribution in gray color map and the number fraction of all misorientation angles with a division value of 10° in two sides of the shear band in rolled sample: (a) tensile and compressive twins distributions in left side; (b) tensile and compressive twins distributions in right side; (c) number fraction of all misorientations in left side; (d) number fraction all misorientations in right side. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
surrounding deformation area compared with the left side during dynamic loading process due to the effect of geometry factor. Therefore, in Fig. 14(a), we highlight the grains which contain twins in right side surrounding deformation area in the yellow rectangle of Fig. 13(b) and measure their 3D sketch maps of matrixes as shown in Fig. 14(a). The a axes of grains suffer compressive stress along normal direction of shearing plane, which could be a beneficial condition for tensile twinning. Furthermore, we calculate the {10–12} < –1011 > tensile twining and {11–22} < 11-2-3 > compressive twining Schmid factors(SF) distribution in inverse pole figure under uniaxial compression. The direction of compressive stress is along SPN. Fig. 14(b) represents SF distribution under SPN compression and inverse pole figure of right side surrounding deformation area in SPN. It can be figured out that, in right side surrounding deformation area where compressive stress mainly exists, grain orientations mostly locate in the area where tensile twining SF is higher and compressive twining SF is lower. The higher of the SF is, the more possible for grains to form twins. Grains in the right side surrounding deformation area are more prone to form tensile twins according to the SF distribution analyses. Thus, the assumption that compressive stress dominates in the right side surrounding deformation area is close to the reality. And it is reasonable to believe that tensile twining more likely to happen in the right side surrounding deformation area.
during dynamic deformation in each side surrounding deformation area. On the contrary, twinning behaves much differently in rolled samples. Fig. 13(a) and (b) show the tensile twins ({10–12} < –1011 > tensile twin) and compressive twins ({11–22} < 11-2-3 > compressive twin) in the left and right side surrounding deformation area, respectively. The misorientations of {10–12} < –1011 > tensile twin boundaries and {11–22} < 11-2-3 > compressive twin boundaries are 85.03° and 64.40°, respectively. Meanwhile, Fig. 13(c) and (d) demonstrate the misorientations distributions in left and right side surrounding deformation areas, respectively. The column in purple represents number fraction of 60–70° and the column in red represents number fraction of 80–90°. The number fraction of 60– 70° is close to the former and the latter column in both surrounding deformation areas. But there is an apparent rising of 80–90° column compared with its former column in right side surrounding deformation area and in the left side only a small rising. These phenomena indicate that tensile twins take the dominating place and more likely happen in right side surrounding deformation area unlike them in annealed samples. Although twinning could occur in previous rolled process and persist till the end of dynamic deformation, we can still consider that twining has happened during dynamic loading. Because the amount of twinning should approximately be the same in both sides if there is no twining process activated during dynamic loading. This remarkable phenomenon that tensile twins are more likely to be activated in the right side surrounding deformation area is leaded by the combined function of stress and grain orientation. Since that the hat-brim part suffers compression from the hat-body part, it can be assumed that compressive stress plays a great role in right side
4. Conclusions Dynamic behaviors of rolled and annealed pure titantium hat-shaped samples have been systematically investigated and 104
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Fig. 14. Analyses of tensile twinning behavior in hat-brim side of rolled sample: (a) three highlighting grains with tensile twins in the yellow rectangle in Fig. 13(b) and their 3D orientation diagrams of matrixes; (b) inverse polar map of right side surrounding deformation area in SPN and {10–12} < –1011 > tensile twining and {11–22} < 11-2-3 > compressive twinning Schmid factors distributions under SPN compression.
grains in the hat-brim suffer more compressive stress than the grains in the hat-body. In the deformation region around the shear band, {10–12} < –1011 > tensile and {11–22} < 11-2-3 > compressive two types twins are observed in both state samples and {10–12} < –1011 > tensile twins are more frequently observed in rolled sample. In the rolled sample, {10–12} < –1011 > tensile twins are more likely to happen in the hat-brim side than hat-body side due to the difference of stress state in two sides.
discussed by EBSD technique in this study, including microstructure, texture, and twining distinction within surrounding deformation area. There have some similarities in microstructure and the texture characteristic within adiabatic shear band while the differences of initial structure induce some significant distinctions in dynamic stress-strain response, morphology features and twining behaviors. The major conclusions can be summarized as followings: 1. Both the stress-strain response curves of rolled and annealed samples have three stages: strain hardening stage, shearing instability stage and dynamic equilibrium stage. But the peak stress of rolled sample is much higher than the other due to the effect of wordhardening and the stress collapse occurs in much shorter time. Besides, the annealed curve has a slowly stress decreasing stage at the peak stress in where the sample stores energy to overcome the ASDE for the subsequent shear banding process. The dynamic shear response reveals that rolled sample shows a higher susceptibility of adiabatic shear localization compared with the annealed one. 2. RDRX can happen in both state samples by the calculation in thermodynamic and kinetic. In spite of the difference of initial structure, the microstructure within both adiabatic shear bands have the similar equiaxed ultrafine grains and texture features, that is, the < 11–20 > direction and the {10-10} plane of the grains tend to parallel with the macro local shear direction and shear plane, respectively. 3. Due to the changing of geometric shape during dynamic loading,
Acknowledgement The authors would like to thank National Natural Science Foundation of China (NSFC) for the financial support (Project 50871125). The work reported was also supported by the National Key Laboratory Foundation for Powder Metallurgy of Central South University (Project 2008112047). References [1] T.W. Wright, The Physics and Mathematics of Adiabatic Shear Bands, Cambridge University Press, Cambridge, 2002. [2] Y. Xu, Y. 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) 737–744. [3] M.A. Meyers, Y.B. Xu, Q. Xue, M.T. Pe´rez-Prado, T.R. McNelley, Microstructural evolution in adiabatic shear localization in stainless steel, Acta Mater. 51 (2003)
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Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Adiabatic shear behaviors in rolled and annealed pure titanium subjected to dynamic impact loading
MARK
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Lianjun Kuang, Zhiyong Chen , Yanghui Jiang, Zhiming Wang, 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: Shear bands Titanium Microstructure Twinning Dynamic recrystallization
The hat-shaped samples cut from rolled and annealed titanium plates were prepared to explore the adiabatic shear behaviors subjected to high-strain-rate deformation operated via Split Hopkinson Pressure Bar. The dynamic shear response calculation reveals that dynamic deformation processes of both state samples can be divided in similar three stages but rolled sample shows a higher susceptibility of adiabatic shear localization compared with the annealed one. Optical microscopy and electronic backscatter diffraction technique (EBSD) were used to systematically analyze the microstructure and texture characteristics. The results show that adiabatic shear bands form in both state samples and rotational dynamic recrystallization (RDRX) occurs within shear area and results in the formation of ultrafine equiaxed grains. Furthermore, ultrafine equiaxed grains within adiabatic shear bands have the same texture feature that < 11–20 > direction and {10-10} plane parallel to macro local shear direction and shear plane respectively. In the deformation region around the shear band, {10–12} < –1011 > tensile and {11–22} < 11-2-3 > compressive two types twins are observed in both state samples and {10–12} < –1011 > tensile twins are more frequently observed in rolled sample. In the rolled sample, {10–12} < –1011 > tensile twins are more likely to happen in the hat-brim side than the hat-body side due to the difference of stress state in two sides.
1. Introduction Shear localization is a common phenomenon for metallic materials under high-strain-rate deformation such as penetration and it always goes with the formation of shear band. Shear localization can be regarded as adiabatic process because the heat within the narrow shear band area is hard to diffuse in extremely short time [1]. Thus, this process is also called adiabatic shear localization. Besides, adiabatic shear localization is one of the important failure mechanisms of materials under high-strain-rate deformation, which makes it closely related to the service life limit of material [2]. Therefore, numerous studies have been conducted on adiabatic shear localization of various metals and alloys, including steel, magnesium, titanium, copper, aluminum and so on [3–9]. And, in particular, the advantages of titanium and its alloys make them popular in various industries: medical applications (for the excellent biocompatibility), offshore applications (for the superior corrosion resistance), military and aerospace applications (for the high specific strength) and sports equipment, etc. [10]. As titanium and its alloys used in military and aerospace usually suffer extreme conditions such as high speed impact, adiabatic shear localization contributes to the failure of materials a lot.
⁎
And it is easy to form adiabatic shear band in titanium and its alloys under dynamic loading because of their low thermal conductivity [11,12]. Hence, adiabatic shearing behaviors of titanium and its alloys, including microstructural evolution and theoretical explanation, have been extensively investigated by simulation research and experimental study during recent decades [13–18]. Zherebtsov et al. and Yang et al. reported that, in deformed titanium, there are ultrafine nano-size grains within the adiabatic shear band after dynamic loading [19,20]. Besides, Chichili et al. investigated microstructure in annealed polycrystalline titanium subjected to dynamic deformation and Meyers et al. proposed rotational dynamic recrystallization (RDRX) theory based on the nano-size equiaxed grains with low density of dislocations within adiabatic shear band [21,22]. In addition, Rittel et al. reported that dynamic recrystallization (DRX) not only precedes adiabatic shear failure but it is also likely to be a dominant micromechanical factor in the very generation of the band [23]. Nevertheless, the differences of microstructural evolution processes between deformed and annealed original structure of identical component titanium have not been systematically studied. Sun et al. suggested that deformation stored energy has significant effects on the final average grain size in the
Corresponding author. E-mail address: [email protected] (Z. Chen).
http://dx.doi.org/10.1016/j.msea.2017.01.011 Received 8 December 2016; Received in revised form 28 December 2016; Accepted 3 January 2017 Available online 04 January 2017 0921-5093/ © 2017 Elsevier B.V. All rights reserved.
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solution of 4 ml hydrofluoric acid +20 ml nitric acid +200 ml distilled water. Samples for EBSD, cutting at the maximum diameter of the hap-shape, were primarily mechanical grinded by using different grit papers with particle sizes from 400 to 2000 mesh, then electrolytic polished on a twin-jet polisher in a solution of 10 ml perchloric acid +70 ml n-Butyl alcohol +120 ml methanol at 90 V and −20 °C for 90 s. The SEM picture of twin-jet samples for EBSD is illustrated in Fig. 1(c). EBSD studies were carried out on a FEI Helios Nanolab 600i scanning electron microscope equipped with an orientation imaging microscopy software developed by HKL system. High resolution EBSD measurements were obtained using a step size of 120 nm while the macro area scans used a step size of 2 µm. Channel 5 software was used for microstructure and microtexture analyses based on EBSD data. The misorientations of grain boundaries, which are greater than 15°, are defined as high-angle grain boundaries (HAGBs) in this study while those in the range of 2–15° are defined as low-angle grain boundaries (LAGBs).
adiabatic shear band, which indicated that deformation stored energy in rolled titanium takes some significant effects on microstructure after dynamic deformation [24]. Moreover, Yang et al. reported that the early stage of shear localization involves the formation and multiplication of mechanical twins, giving rise to the twin/matrix lamellar structure aligned along the shear direction [25]. However, the studies focusing on microstructure and microtexture characteristics of adiabatic shear band in deformed titanium with elongating grains and annealed titanium with equiaxed grains are still relatively scanty. The aim of the present work is to perform macroscopic and microscopic investigations of the shear bands and surrounding deformation areas in both rolled and annealed titanium hat-shaped samples via optical microscopy (OM) and electron backscatter diffraction (EBSD) technique. This makes it possible to compare the differences of dynamic behaviors between the two state titanium samples. Specifically, most of the efforts have been focused on the dynamic stress-strain responses, macroscopic morphology of shear bands, microstructure with shear bands and twinning in the surrounding deformation areas. It is worth to be noted that the current study investigates the texture characteristics of shear bands in rolled and annealed titanium of identical component, which are rarely reported in the past researches. Besides, the distinctions of twinning behaviors in different surrounding deformation areas are discussed in this study. This research advances our understanding on adiabatic shear behaviors in different original state titanium and enhances the comprehending of microstructural deformation mechanism.
3. Results and discussions 3.1. Shear stress-shear strain response Since the hat-shaped samples were experimented by a Split Hopkinson Pressure Bar, the shear stress and shear strain in the shear area could be calculated from the data collected by the strain gauge recordings on the incident bar and transmitter bar. The calculation equations were provided by Andrade et al. [26] and displayed as the followings:
2. Experimental
E 0A ε t (t) ⎧ τ= ⎛ d s+ d ⎞ ⎪ π h⎜ 1 2 ⎟ ⎪ ⎝ 2 ⎠ ⎪ ⎨ 2 C0 ∫ t[εi(t) − εt(t)]dt 0 ⎪ γ= w ⎪ 2C 0[ε i(t) − ε t (t)] ⎪ γ̇= ⎩ w
A forged commercially pure α titanium block with the size of 200 mm×80 mm×60 mm was preheated for 50 min at 1103 K, then were rolled to 12 mm in the thickness direction via 7 paths. The final cumulative reduction reached 80%. Then the hot-rolled plate was cut into two pieces, one was placed for the following cutting process and the other was annealed at 1023 K for 120 min in the vacuum furnace after the rolling. Hat-shaped samples (as illustrated in Fig. 1(a)) used in this study were cut from the former rolled plate and the annealed plate, respectively. Both rolled and annealed samples were cut along the normal direction of the titanium plate for the subsequent high-ratestrain deformation. In this step, three same samples were prepared for each state and later tests or investigations are applied to all the samples to avoid accidental errors. Dynamic tests were carried out using a Split Hopkinson Pressure Bar (SHPB) at room temperature. Samples for microstructure characterization were cut from the dynamically deformed hat-shaped samples along the loading axis by wire-electrode cutting (as illustrated in Fig. 1(b)). Metallographic specimens were prepared by standard mechanical polishing and then etched in a
(1)
The shear stress-shear strain curves of rolled and annealed samples obtained from the former equations, shown in Fig. 2, indicate similar stages of dynamic responses with obvious differences in each stage. In this graph, a1, b1, c1 are the points on the rolled state curve and a2, b2, c2, d2 are the points on the annealed state curve. Both the dynamic deformation processes can be divided into three stages: strain hardening stage (0~a1, 0~a2), shearing instability stage (a1~b1, a2~b2), dynamic equilibrium stage (b1~c1, b2~c2). In the first stage, the shapes of two state curves are similar to each other, which indicates that deformation modes of titanium in the strain hardening stage of two state samples are the same to some extent. Here, shear stress increases with the increasing of shear strain from
Fig. 1. Schematic map of hat-shaped sample and EBSD sample: (a) schematic diagram of hat-shaped sample for dynamic loading; (b) schematic diagram of samples cut along the loading axis direction; (c) SEM picture of twin-jet sample for EBSD experiment.
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dissipation energy (ASDE) proposed by Grady [27]. The formation and expansion of adiabatic shear band need to overcome an energy barrier. And the higher for the barrier, the harder for the formation of adiabatic shear band, namely the adiabatic shear sensitivity is weaker. The value of ASDE can be calculated in the following equation: 1
⎛ ⎞4 ρ c 9ρ3cλ3 Γ= ⎜⎜ 3 2 ⎟⎟ α ⎝ τ γα γ̇ ⎠
(2)
In the above equation, Γ represents ASDE, ρ is material's density, c is the specific heat capacity of material, λ is thermal diffusivity which reflects the heat dissipation ability, α is thermal softening coefficient, γ̇ is strain velocity, τγ is the flow stress at γ̇ velocity. Among them, ρ, c, λ and α describe inherent properties of materials, so they keep to be constants regardless of the initial state for a same material at a same loading condition. But flow stress of different initial state samples shows quite different value. Annealed sample get a relatively lower flow stress just before the collapse, therefore its ASDE is much higher than the rolled one. In addition, due to the lack of deformation stored energy, annealed sample needs longer time to deform for energy storing. Meanwhile, the softening effect caused by deformation heat can counteract work-hardening at that stress value, so there is a slowly stress decreasing stage before collapse in annealed curve.
Fig. 2. True stress-strain curves of rolled and annealed samples obtained from Hopkinson tests.
0 to approximate 1.2 until achieving the peak stress. The corresponding strain of the peak point is where the plastic instability stage appears. In the next stage, shear stress decreases sharply with the increasing of shear strain which called stress collapse. The emergence of stress collapse is mainly caused by the dominant status of thermodynamic softening in the competition with work-hardening. Adiabatic shear band starts to form in this stage. In the final dynamic equilibrium stage, thermal softening effect induced by the working heat is equal to hardening effect induced by the deformation, which results in a platform at about 430 MPa shown in the curves for both rolled and annealed samples. And it is interested that the values of the platform in two state curves are almost the same in spite of the differences in the former two stages. However, there are obvious differences in each stage between rolled and annealed samples. At the end of first stage, the rolled sample curve reaches higher top flow stress of about 1150 MPa while the peak flow shear stress of annealed sample is only about 1000 MPa, which could be the result of work-hardening effect. In the second stage, the stress collapse of the rolled sample happened at higher stress and the magnitude of the collapse is greater as well, which indicates that the rolled sample shows higher adiabatic shear sensitivity. Stored energy has important effects on the dynamic loading process [24]. Stored energy in the rolled sample releases while stress collapsing, therefore the formation of adiabatic shear band could be easier because of the energy supplement. Besides, we discover that there is a slowly stress decreasing stage (a2~d2) before shear instability in the annealed curve (as shown in the Fig. 2). The appearance of this stage is related to the initial structure. This phenomenon can be explained using the adiabatic shear
3.2. Macroscopic characteristics 3.2.1. The whole morphology The original structure of annealed sample contains equiaxed grains with an average grain size about 24 µm while the original structure of rolled sample consists of elongated grains (as illustrated in Fig. 3). And the structures of both state samples after dynamic impact have changed especially in the area where forced shear stress concentrates. Fig. 4(a) and (b) illustrate the whole view of adiabatic shear bands and their adjacent areas of rolled and annealed samples via optical microscope. The location of adiabatic shear band in the hat-shaped sample is shown in Fig. 1(b). Adiabatic shear bands form in both state samples and contain significant different structure compared with the adjacent areas. The widths of the shear bands in the two state samples gradually narrow down along the shear direction from the top to the bottom. The widest area can reach around 50 µm while the narrowest area is only about 20 µm. For the adjacent area, structure in the rolled sample inherits rolling feature with lamellar structure and the anneal one still consists of coarse grains. This phenomenon indicates the dramatical shear localization in the shear area. Cracks take place in the two state samples and occur in the ends of adiabatic shear band prior to the adjacent deformation areas. And in every single shear band, crack in the bottom extends more deeply in the shear band along the shear direction while crack in the top extends just a little in the shear band.
Fig. 3. Structures of rolled and annealed plates via optical microscopy: (a) rolled sample; (b) annealed sample.
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contain adiabatic shear bands and the surrounding areas (scanning pace 0.5 µm). We can divide them into two zones due to the grains’ orientation and morphology: adiabatic shear band and surrounding deformation area. The approximate boundaries of these two zones are indicated in white dotted line in Fig. 5. Adiabatic shear bands in both state samples are all filled up with ultrafine grains and need more detailed scanning. The surrounding deformation areas in two sides of the shear band are quite different. In rolled sample, the angle between elongating direction of right side grains and shear direction is quite different from the other side. In annealed sample, grains in the left side are elongated along shear direction apparently while grains in the right side still have some features of equiaxed grains (such as trigeminal grain boundaries). Herein, twins (indicated via black arrows in Fig. 5) in both states are quite clearer than them in Fig. 4 and twins in the surrounding deformation area of rolled sample are observed. Twins observed in Figs. 4 and 5 demonstrate that twinning plays a great role in the deformation of the surrounding deformation areas during dynamic loading. And twinning behavior is deep discussed in the later Section 3.4.
Fig. 4. The whole view of shear band in two state samples via optical microscopy: (a) the shear band in rolled sample; (b) the shear band in annealed sample.
Besides, the shape of the crack in the rolled sample is approximate a straight line while the crack in the annealed sample is serrated. It should be noted that there are apparent twins (some of them are indicated via black arrows in Fig. 4(b)) in the adjacent area of annealed sample and it need more detailed investigating method to affirm whether there are twins in adjacent area of rolled sample.
3.3. Adiabatic shear band 3.3.1. Microstructure characteristics The adiabatic shear band microstructure of rolled and annealed samples are shown in Fig. 6(a) and (b) respectively. Shear bands in both state samples are filled up with ultrafine grains with several LAGBs in the grains. The range of grain sizes within shear band of annealed and rolled states are both about 0.1–1 µm. The formation of the ultrafine grains in the shear band is caused by the heavy deformation and recrystallization. Meanwhile, as we all know that shear band area suffers much higher strain than its surrounding area during dynamic process, which results in significant temperature rise and induces grain coarsening. The range of the grain size is the
3.2.2. The fractional morphology We use EBSD data to represent the grain orientation relationship for the fractional morphology and further analyses in this study. All orientation maps presented in this paper use the inverse pole figure coloring mode at the corner of the Fig. 5, in which the red, blue and green color represents < 0001 > , < 10-10 > and < 11–20 > direction, respectively. HAGBs and LAGBs are indicated by black lines and white lines, respectively. Fig. 5 shows the EBSD maps of rolled and annealed samples, which
Fig. 5. Macroscope EBSD maps of shear band and surrounding area in rolled sample and annealed sample: (a) rolled sample; (b) annealed sample. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
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Fig. 6. Microstructure of adiabatic shear bands in both state samples: (a) shear band in rolled sample; (b) shear band in annealed sample; (c) amplification of elongated grain within the rectangle area in rolled sample; (d) amplification of elongated grain within the rectangle area in annealed sample; (e) misorientations distribution map point to point along the green line in the elongated grain in (c). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
represent shear direction, normal direction and normal direction of shear plane, respectively. The pole figures suggest that grains in the adiabatic shear band have the similar texture characteristic in spite of the different initial microstructure in the shear area. The final orientation of the grains in the adiabatic shear band can be described as followings: the < 11–20 > direction and the {10-10} plane of the grains tend to parallel with the macro local shear direction and shear plane respectively.
outcome of grain refinement and coarsening. Although most of the ultrafine grains are equiaxed, some elongated fine grains are investigated in the shear bands. Fig. 6(c) and (d) represents the elongating grains within the rectangle area in Fig. 6(a) and (b), respectively. And Fig. 6(e) illustrates the misorientation along the green line in the elongating grain shown in Fig. 6(c). The five peaks in the diagram are in correspondence with the five LAGBs along the green line within the grain. This grain is surrounded by fragmentized small grains and irregularly divided into subgrains or substructures of various sizes by the LAGBs inside the grains. The peaks and misorientations of other values reveal the inhomogeneous deformation inside the grain during dynamic loading and formation of deformation cell structures. In Fig. 6(d), subgrain boundaries composed of LAGBs and HAGBs are found in the rectangle area named A and B, which reveals that the HAGBs in the elongated grain are grown from LAGBs and finally lead the subgrains growing into fragmentized fine grains like the surrounding area. Except the microstructure, texture of shear bands is also measured by the detailed EBSD scanning. The pole figures of these two state samples are illustrated in Fig. 7(a) and (b). The SD, ND and SPN
3.3.2. Temperature rising within the ASB Shear localization can be regarded as adiabatic process because the heat within the narrow shear band area is hard to diffuse in extremely short time. The microstructural evolution associated with the dynamic deformation is greatly influenced by the temperature rising during the adiabatic shear banding. And the temperature can be calculated by the following equation [28]:
T=
99
β C vρ
γ
∫ 0
τdγ +T0 (3)
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Fig. 7. The {0001}, {11–20} and {10-10} pole figures in shear band zone and the extracted 3D orientation diagrams of (a) rolled sample; (b) annealed sample.
Fig. 8. Temperature rising curve with stress-strain response curve of two state samples within the shear band: (a) rolled sample; (b) annealed sample.
where, β is the heat-converting factor (0.9) that represents the fraction of plastic energy converting to heat, ρ is the mass density of titanium (4510 kg/m3), Cv is the heat capacity (523 J/K), T0 is the room temperature (298 K), γ is the flow stress and τ is the flow strain, respectively. Temperature rising curves of two state samples are illustrated in Fig. 8 by substituting the dynamic response data during forced plastic deformation into Eq. (3). In both state samples, temperature increases with the increasing of strain. And temperature increases fast at first then increases relatively slowly and increases with an approximately constant velocity till the end. And the temperature in shear band area of rolled sample reaches ~700 K (equal to ~0.36Tm) at shear strain ~1.1 where shear instability occurs (point a1 shown in Fig. 8(a)) while the annealed reaches ~900 K (equal to ~0.46Tm) when the shear strain increase to ~1.8 where shear instability occurs (point a2 shown in Fig. 8(b)). These calculating results indicate that the temperature in the adiabatic shear band area meets the needs of recrystallization of
titanium. And in the subsequent cooling procedure, it only takes several microseconds (μs) to cool to room temperature according to the estimation by using the classical Fourier heat conduction equation [29]. Therefore, after the dynamic deformation, the microstructure in the adiabatic shear band formed at high temperature can be preserved. 3.3.3. Grain refinement mechanism Adiabatic environment and extremely short time are the two important features in shear banding, which makes the dynamic recrystallization (DRX) here quite different from the traditional DRX process. Early in 1997, it was reported by Hines et al. [28] that the DRX happened in shear band was essentially different from the classical DRX especially for the process of high-angle boundary migration and subgrain coalescence which would take a much more time to accomplish. The most accepted recrystallization mechanism in the adiabatic shear band, rotational dynamic recrystallization (RDRX), was presented by Meyers et al. [22,30]. According to RDRX 100
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where, θ is the rotation angle for subgrain boundaries (0–30°); L is the size of the subgrain; k (equal to 1.38×10–23 J/K) is the Boltzmann constant; T is the temperature in the shear band; t is the time for the rotation of subgrain; δDGB is the grain boundary diffusion coefficient and it was experimentally measured by Herzig et al. [31]:
⎡ -153kJmole-1 ⎤ ⎥(m2/s) δDGB=9.2 ×10-14exp⎢ RT ⎣ ⎦
(5)
γb is the grain boundary energy as a function of misorientation that can be calculated by the Read-Shockley equation [32]:
γb=
mechanism, the grains in the adiabatic shear band area experience grain elongating, grain breaking-up and subgrain rotation and the kinetic condition can be described as following equation [30]:
LkT
t=
(6)
where, G (=440 GPa) is shear modulus; b (=0.295 nm) is the module of Burgers vector; α=4; ν=0.33; θ is the misorientation angle between two adjoining lattices which always considered as 15°. The results of Eq. (4) (as shown in the Fig. 9) illustrate the time that subgrains of five different sizes (L=0.1 µm, 0.3 µm, 0.5 µm, 0.8 µm and 1.0 µm) rotate from 0 to 30° needs at 900 K (0.46Tm). Although, in rolled sample, the temperature at plastic instability has not reached 900 K, the temperature increases to more than 900 K rapidly in the subsequent deformation. It is found that the rotation of sub boundaries by an angle of 30° can be accomplished within deformation time (80 μs) when the sizes of the subgrains is less than 1 µm. The grains size within adiabatic shear band in this study is from 0.1 to 1 µm and the temperature in the shear band area is more than 900 K. Therefore, it's reasonable to believe that, in kinetic,
Fig. 9. Angle of rotation of subgrain boundary in titanium as a function of time for different subgrain sizes (L=0.1 µm, 0.3 µm, 0.5 µm, 0.8 µm and 1.0 µm) at 0.46Tm.
4 δDGBγb
Gb θ[1 +ln(α/2 π)-lnθ] 4 π(1 - ν)
3tanθ- 2cosθ 4 3 2 + 3 2 4 3 tan(θ/2)- 2 - 3 ln + + ln 3 - 6sinθ 9 9 tan(θ/2)- 2 + 3 2- 3 3 (4)
Fig. 10. Presentation of elongation of grains in hat-body side and tilting in hat-brim side: (a) the angle between elongating direction of grains and shear direction in initial rolled sample; (b) the angle between elongating direction of grains and shear direction in hat-body side of rolled sample; (c) the whole cross section picture of rolled sample; (d) the whole cross section picture of annealed sample.
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Fig. 11. Tensile twins and compressive twins in rolled and annealed samples: (a) tensile twin in rolled sample; (b) compressive twin in rolled sample; (c) misorientations distribution along line L1; (d) misorientations distribution along line L2; (e) tensile twin in annealed sample; (f) compressive twin in annealed sample; (g) misorientations distribution along line L3; (h) misorientations distribution along line L4.
3.4. Surrounding deformation area characteristics
the occurrence of the RDRX mechanism within the ASB is possible. In summary, the calculation in thermodynamic and kinetic reveals that the rotational dynamic recrystallization can occur theoretically and the observation by EBSD method demonstrates that RDRX actually happens in the adiabatic shear band area.
3.4.1. Morphology features The left side surrounding deformation area in EBSD maps shown in Fig. 5 represents hat-body area (as shown in Fig. 1(a) and (b)) in the 102
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Fig. 12. Tensile twins and compressive twins in two sides of the shear band in annealed sample: (a), (b) for the IPF and IQ map of left side; (c), (d) for the IPF and IQ map of right side. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
because of the compression from the hat-body. In summary, deformations of left and right side surrounding deformation areas are quite different in both state samples. But the diversities of two sides surrounding deformation area show some similar features to some extent. Besides, the stress state of hat-brim and hat-body areas are no more simple shear because of the geometrical changing of hat-shaped samples during dynamic loading.
original hat-shape samples and the other side represents hat-brim area. The grains in hat-body area in both state samples are all elongated along the shear direction. It's much more obvious in the annealed sample. However, it needs further analyses for rolled sample although the grains are typical elongating structure. Because the elongating direction of grains in original rolled sample is vertical to normal direction of the plate, which causes that grains have a certain angle to the shear direction in the initial structure before dynamic loading (as shown in Fig. 10(a)). To ensure that whether the grains tilt to shear direction or not, we measure the angle between elongating direction of hat-body grains and the shear direction in the hat-shaped sample after dynamic loading in Fig. 10(b). The angle decreases to 40° even less in the area near shear band while the angle still maintains at about 58° in the zone far away from shear band (about 100 µm far away from shear band). Due to the above analyses, we can affirm that hat-body grains just near the shear band in both state samples have the tendency tilting to shear direction. In addition, the features of grains in hat-brim area are quite different from the hat-body area. This phenomenon is caused by the changing of geometric conditions during the dynamic deformation. Fig. 10(c) and (d) show the whole cross section of the hat-shape samples, (c) represents rolled sample, (d) represents annealed sample. The geometries of hat-shaped samples have changed a lot after dynamic loading, especially the hat-brim parts. We can find that hatbrim rotates towards the outside due to compression of hat-body in Fig. 10(c). That is why the angle between grains elongating direction and shear direction increases to almost 90° in hat-brim area. Besides, hat-brim suffers compression from hat-body to outside. In this case, Hat-brim suffers not only shear stress but also the compressive stress
3.4.2. Twinning behavior Appearance of twins in both state samples indicates that twinning plays a great role in the dynamic deformation. The analysis on the categories of twins is based on misorientation relationship obtained from EBSD data. Fig. 11(a)-(d) illustrate the tensile and compressive twins in rolled sample and misorientations distributions along L1 and L2 while (e)-(h) illustrate twins and misorientations distributions in annealed sample. Fig. 11(a) and (c) indicate {10–12} < –1011 > tensile twin corresponding to 85° < 11–20 > boundaries and Fig. 11(b) and (d) indicate {11–22} < 11-2-3 > compressive twin corresponding to 64.4° < 10-10 > boundaries in rolled sample. Fig. 11(e)-(h) indicate the same tensile and compressive twins in annealed sample as well. These two types of twins are most frequently observed in this study. Fig. 12 illustrates the twins under different background colors (IQ color and IPF color) in annealed sample including left and right side surrounding deformation areas. Red lines represent tensile twins ({10–12} < –1011 > tensile twin) and blue lines represent compressive twins ({11–22} < 11-2-3 > compressive twin). It can be found that both tensile and compressive twinning have been activated 103
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Fig. 13. Tensile and compressive twin distribution in gray color map and the number fraction of all misorientation angles with a division value of 10° in two sides of the shear band in rolled sample: (a) tensile and compressive twins distributions in left side; (b) tensile and compressive twins distributions in right side; (c) number fraction of all misorientations in left side; (d) number fraction all misorientations in right side. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
surrounding deformation area compared with the left side during dynamic loading process due to the effect of geometry factor. Therefore, in Fig. 14(a), we highlight the grains which contain twins in right side surrounding deformation area in the yellow rectangle of Fig. 13(b) and measure their 3D sketch maps of matrixes as shown in Fig. 14(a). The a axes of grains suffer compressive stress along normal direction of shearing plane, which could be a beneficial condition for tensile twinning. Furthermore, we calculate the {10–12} < –1011 > tensile twining and {11–22} < 11-2-3 > compressive twining Schmid factors(SF) distribution in inverse pole figure under uniaxial compression. The direction of compressive stress is along SPN. Fig. 14(b) represents SF distribution under SPN compression and inverse pole figure of right side surrounding deformation area in SPN. It can be figured out that, in right side surrounding deformation area where compressive stress mainly exists, grain orientations mostly locate in the area where tensile twining SF is higher and compressive twining SF is lower. The higher of the SF is, the more possible for grains to form twins. Grains in the right side surrounding deformation area are more prone to form tensile twins according to the SF distribution analyses. Thus, the assumption that compressive stress dominates in the right side surrounding deformation area is close to the reality. And it is reasonable to believe that tensile twining more likely to happen in the right side surrounding deformation area.
during dynamic deformation in each side surrounding deformation area. On the contrary, twinning behaves much differently in rolled samples. Fig. 13(a) and (b) show the tensile twins ({10–12} < –1011 > tensile twin) and compressive twins ({11–22} < 11-2-3 > compressive twin) in the left and right side surrounding deformation area, respectively. The misorientations of {10–12} < –1011 > tensile twin boundaries and {11–22} < 11-2-3 > compressive twin boundaries are 85.03° and 64.40°, respectively. Meanwhile, Fig. 13(c) and (d) demonstrate the misorientations distributions in left and right side surrounding deformation areas, respectively. The column in purple represents number fraction of 60–70° and the column in red represents number fraction of 80–90°. The number fraction of 60– 70° is close to the former and the latter column in both surrounding deformation areas. But there is an apparent rising of 80–90° column compared with its former column in right side surrounding deformation area and in the left side only a small rising. These phenomena indicate that tensile twins take the dominating place and more likely happen in right side surrounding deformation area unlike them in annealed samples. Although twinning could occur in previous rolled process and persist till the end of dynamic deformation, we can still consider that twining has happened during dynamic loading. Because the amount of twinning should approximately be the same in both sides if there is no twining process activated during dynamic loading. This remarkable phenomenon that tensile twins are more likely to be activated in the right side surrounding deformation area is leaded by the combined function of stress and grain orientation. Since that the hat-brim part suffers compression from the hat-body part, it can be assumed that compressive stress plays a great role in right side
4. Conclusions Dynamic behaviors of rolled and annealed pure titantium hat-shaped samples have been systematically investigated and 104
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Fig. 14. Analyses of tensile twinning behavior in hat-brim side of rolled sample: (a) three highlighting grains with tensile twins in the yellow rectangle in Fig. 13(b) and their 3D orientation diagrams of matrixes; (b) inverse polar map of right side surrounding deformation area in SPN and {10–12} < –1011 > tensile twining and {11–22} < 11-2-3 > compressive twinning Schmid factors distributions under SPN compression.
grains in the hat-brim suffer more compressive stress than the grains in the hat-body. In the deformation region around the shear band, {10–12} < –1011 > tensile and {11–22} < 11-2-3 > compressive two types twins are observed in both state samples and {10–12} < –1011 > tensile twins are more frequently observed in rolled sample. In the rolled sample, {10–12} < –1011 > tensile twins are more likely to happen in the hat-brim side than hat-body side due to the difference of stress state in two sides.
discussed by EBSD technique in this study, including microstructure, texture, and twining distinction within surrounding deformation area. There have some similarities in microstructure and the texture characteristic within adiabatic shear band while the differences of initial structure induce some significant distinctions in dynamic stress-strain response, morphology features and twining behaviors. The major conclusions can be summarized as followings: 1. Both the stress-strain response curves of rolled and annealed samples have three stages: strain hardening stage, shearing instability stage and dynamic equilibrium stage. But the peak stress of rolled sample is much higher than the other due to the effect of wordhardening and the stress collapse occurs in much shorter time. Besides, the annealed curve has a slowly stress decreasing stage at the peak stress in where the sample stores energy to overcome the ASDE for the subsequent shear banding process. The dynamic shear response reveals that rolled sample shows a higher susceptibility of adiabatic shear localization compared with the annealed one. 2. RDRX can happen in both state samples by the calculation in thermodynamic and kinetic. In spite of the difference of initial structure, the microstructure within both adiabatic shear bands have the similar equiaxed ultrafine grains and texture features, that is, the < 11–20 > direction and the {10-10} plane of the grains tend to parallel with the macro local shear direction and shear plane, respectively. 3. Due to the changing of geometric shape during dynamic loading,
Acknowledgement The authors would like to thank National Natural Science Foundation of China (NSFC) for the financial support (Project 50871125). The work reported was also supported by the National Key Laboratory Foundation for Powder Metallurgy of Central South University (Project 2008112047). References [1] T.W. Wright, The Physics and Mathematics of Adiabatic Shear Bands, Cambridge University Press, Cambridge, 2002. [2] Y. Xu, Y. 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) 737–744. [3] M.A. Meyers, Y.B. Xu, Q. Xue, M.T. Pe´rez-Prado, T.R. McNelley, Microstructural evolution in adiabatic shear localization in stainless steel, Acta Mater. 51 (2003)
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