materials Article
Microstructural Evolution in High-Strain-Rate Deformation of Ti-5Al-5Mo-5V-1Cr-1Fe Alloy Chun Ran 1, * 1 2 3
*
ID
, Pengwan Chen 1, *, Zemin Sheng 2 , Jingbo Li 2 and Wangfeng Zhang 3
State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China School of Materials Science and Engineering, Beijing Institute of Technology, Beijing 100081, China;
[email protected] (Z.S.);
[email protected] (J.L.) Beijing Institute of Aeronautical Materials, Beijing 100095, China;
[email protected] Correspondence:
[email protected] (C.R.);
[email protected] (P.C.); Tel.: +86-010-68918108 (C.R.); +86-010-68912470 (P.C.)
Received: 18 April 2018; Accepted: 15 May 2018; Published: 18 May 2018
Abstract: To study the microstructural evolution in high-strain-rate shear deformation of Ti-5Al-5Mo-5V-1Cr-1Fe (Ti-55511) alloy, a series of forced shear tests of hat-shaped specimens have been conducted using a split Hopkinson pressure bar combined with the “strain-frozen” technique. A localized shear band is induced in Ti-55511 alloy in these tests. The experimental results demonstrate that the flow stress in hat-shaped specimens remains constant (about 600 MPa) and is independent of punching depth. The width of the adiabatic shear band increases with increasing punching depth and tends to saturate at 30 µm, and the estimation of the adiabatic shear band (ASB) width in hat-shaped (HS) specimens has been modified. Relying on the experimental results, thermal softening has a minor effect on the onset of the adiabatic shear band and dynamic recrystallization formation, and the nucleation mechanism for dynamic recrystallization is strain-induced boundary migration and subgrain rotation and coalescence. In addition, we suggest the concept of adhesive fracture as the dynamic failure mechanism for Ti-55511 alloy. Keywords: Ti-55511 alloy; forced shear tests; adiabatic shear band; dynamic recrystallization; shear band width
1. Introduction The term “adiabatic shear band” (hereinafter referred to as ASB) has been widely accepted by researchers since it was first mentioned in the original report of Zener and Hollomon in 1944 [1]. ASB is an important failure mechanism of solid materials in high-strain-rate deformation, especially for titanium alloys [2]. The outstanding physical properties of titanium alloys, such as high strength-to-weight ratio, good hardenability and excellent crack growth resistance, have made them into very attractive materials in aerospace, medical equipment and automotive industrial applications [3–6]. A considerable number of investigations on titanium alloys under high-strain-rate loading conditions have been conducted over the last two decades [7–11]. Meyers et al. [7] found a three-fold difference between measured width of ASB and predicted values, calculated by the criterion proposed by Bai et al. [12] and Dodd and Bai [13,14], in commercially pure α-titanium (TA2) hat-shaped (HS) specimens, while the measured width of ASB is slightly higher than the calculated results in Chen et al.’s work [15]. Nanograins with a size of 10–30 nm were observed by Rittel et al. [9], while a subgrain of approximately 200 nm was observed by Meyers et al. [7]. Ti-5Al-5Mo-5V-1Cr-1Fe (Ti-55511) alloy, a typical near-β-type titanium alloy, is superior as an aircraft structural material due to its 15–20% weight loss as compared to Ti-6Al-4V (TC4) alloy [16]. Materials 2018, 11, 839; doi:10.3390/ma11050839
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A considerable number of investigations on Ti-55511 alloy have been conducted over the last five years, and most of them focused on materials fabrication [17–20]. Liang et al. [21] found that the recrystallized volume fraction of Ti-55511 alloy could be quantified as the net softening effect of dynamic recrystallization (DRX) over dynamic recovery mechanisms during hot deformation. Nan et al. [22] pointed out that the influence of strain rate on DRX evolution was the major factor to determine strain-rate sensitivity. However, the findings of Liang et al. and Nan et al. are derived from low-strain-rate loading conditions (100 s−1 ) [16]. Although the main mechanism for adiabatic shear is the competition between the hardening effect (strain and strain rate) and thermal softening effect, the whole process is very complex and involves high strain rates, high local temperature, large plastic deformation and so forth [2]. In fact, the mechanical behavior of Ti-55511 titanium alloy is of great complexity and is strongly sensitive to the loading conditions, such as strain and strain rate [23]. The mechanical behavior and microstructural evolution of Ti-55511 alloy in the dynamic deformation process are still not well understood. The purposes of this study are to gain deeper insights into: (a) dynamic mechanical behavior and microstructural evolution of Ti-55511 alloy in forced shear tests, and (b) the relationship of ASB width between measurement and calculation using the half-width of the shear band criterion proposed by Bai [12] and Dodd and Bai [13,14]. 2. Materials and Methods The Ti-55511 alloy used in the present investigation was in the form of a forged bar with a diameter of 155 mm from the Beijing Institute of Aeronautical Materials, Aero Engine Corporation of China (AECC), PR China. The β-transus temperature of the as-received bars is approximately 1163 K via the metallographic observation method. The chemical composition of the alloy is listed in Table 1. More information of the material has been described previously [16]. Table 1. Chemical composition of Ti-5Al-5Mo-5V-1Cr-1Fe alloy (wt %). Al
Mo
V
Cr
Fe
C
N
H
O
Zr
Si
Ti
5.50
4.82
4.82
1.02
1.02
0.02
0.03
0.001
0.1
0.15
0.10
balance
A series of dynamic forced shear tests were carried out at 293 K by means of the split Hopkinson pressure bar (SHPB, School of Aeronautics, Northwestern Polytechnical University, Xi’an, China) technique using hat-shaped (HS) specimens [7,24]. This specially designed specimen configuration allows the creation of a well-controlled localized shear band region during deformation, and has been successfully used in the studies of large strain, high-strain-rate deformation of metals in conditions of forced localized shear [15,25–27]. The samples were sandwiched between the incident and transmission bars during SHPB tests. High-strength steel stopper rings were used to ensure a prescribed displacement in the principal plastic deformation region (see Figure 1). The HS specimens were machined from the forged bar using electrical discharge machining (EDM) (Jiangsu Taizhou Chuang yuan Machine Tool Co., Ltd., Taizhou, China) and a numerical control milling machine (Hebei Huayue Machinery Manufacturing Co., Ltd., Xingtai, China), where details of the experimental setup were described previously [16]. Different shear strains were obtained by varying the punching depths (Pd ), that is, the thickness of the stopper ring, as depicted in Figure 1. The values of Pd were prescribed as 0.7, 0.8, 0.9, 1.0 and 1.1 mm, respectively. It should be pointed out that the bar–specimen interfaces were sufficiently lubricated in order to reduce friction and specimen barreling. It also should be pointed out that we just focus on the microstructural evolution of Ti-55511 alloy after ASB formed in this work, and three HS specimens were used for each loading condition. The velocity of the striker, v, can be calculated as the distance of the photo diode (a) divided by the time (t) recorded by a data acquisition instrument. The stress state in the plastic deformation region is fairly close to simple shear loading.
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Figure 1. In-plane dimensions of the HS specimen (dimensions (dimensions in in mm). mm).
The samples samples for for microstructural microstructural observation observation were were cut cut parallel parallel to to the the deformation deformation direction direction by by The EDM, and metallographic specimens were prepared by standard mechanical polishing and etched in EDM, and metallographic specimens were prepared by standard mechanical polishing and etched Kroll’s reagent. Scanning electron in Kroll’s reagent. Scanning electronmicroscopy microscopy(SEM) (SEM)and andtransmission transmissionelectron electron microscopy microscopy (TEM) (TEM) specimens were prepared from different loading conditions to allow a comparative characterization specimens were prepared from different loading conditions to allow a comparative characterization of the the microstructure. microstructure. The The observation observation was the center center of of the the shear shear region region (dotted (dotted circle circle of was focused focused on on the shown in Figure 1). The samples for TEM observation were first polished to a thickness of about 50 shown in Figure 1). The samples for TEM observation were first polished to a thickness of about 50 µm, μm, and then a 3-mm-diameter foil was carefully perforated from the samples, followed by and then a 3-mm-diameter foil was carefully perforated from the samples, followed by ion-beam ion-beam Gatan 691 Inc., Blvd., Las Positas Blvd.,CA, Pleasanton, CA, USA) precision milling in amilling Gatan in 691a (Gatan Inc., (Gatan Las Positas Pleasanton, USA) precision ion-polishing ion-polishing system at 5 KeV with a final polishing step at 3 KeV of ion energy. Optical microscopy system at 5 KeV with a final polishing step at 3 KeV of ion energy. Optical microscopy (OM) and SEM (OM) and SEM were performed LEICA DMI Kirana-05M (Leica examinations were examinations performed on LEICA DMI 3000Mon Kirana-05M (Leica3000M Microsystems CMS GmbH, Microsystems CMSand GmbH, Wetzlar, Germany) and HITACHI S-4800 (Hitachi Chiyoda-ku, High-Technologies Wetzlar, Germany) HITACHI S-4800 (Hitachi High-Technologies Corporation, Tokyo, Corporation, Chiyoda-ku, Tokyo, Japan), respectively. TEM observations were conducted in a FEI 2 Japan), respectively. TEM observations were conducted in a FEI Tecnai G -F30 (FEI Corporation, Tecnai G2-F30 OR, USA) transmission electron Hillsboro, OR, (FEI USA)Corporation, transmissionHillsboro, electron microscope operating at 200 kV. microscope operating at 200 kV. 3. Results and Discussion 3. Results and Discussion 3.1. Mechanical Tests 3.1. Mechanical Tests When one-dimensional stress waves in the bars are achieved and the specimen is in a state of uniform stress, the histories ofstress applied force (distributing on the upper surface of the is HS When one-dimensional waves inFthe bars are achieved and the specimen inspecimen) a state of and punching Pd in the can be determined by: uniform stress,depth the histories ofspecimen applied force F (distributing on the upper surface of the HS specimen) and punching depth Pd in the specimen can be determined by: Fs (t) = A0 E0 [ε i (t) + ε r (t) + ε t (t)]/2 (1) Fs ( t= ) =AA00EE00ε[tε(i t()t ) + ε r (t ) + ε t (t )] 2 , , (1) = A0 E0ε t (t ) Z t
Pd (t) = −2C0 t ε r (t)dt, (2) Pd ( t ) = −2C0 0ε r ( t ) dt , (2) 0 where A0 is the cross-sectional area of the bars, and E0 and C0 are Young’s modulus and elastic bar wherespeed A0 is of thethe cross-sectional area of the bars, and E0 εand C0 are Young’s modulus and elastic bar wave bar material, respectively. Here, εi (t), r (t) and εt (t) represent incident, reflected and wave speedstrain of thehistories bar material, Here, εi(t), εr(t) and εt(t) represent incident, reflected transmitted in the respectively. bars at the specimen ends, respectively. and transmitted strain histories in the bars at the specimen ends, Then, the shear stress (τ s ), global shear strain (γ), local shearrespectively. strain (γloc ) and local shear strain . stress (τscan ), global shear strain rate (Then, γ ) ofthe theshear HS specimen be estimated as: (γ), local shear strain (γloc) and local shear strain loc
rate ( γloc ) of the HS specimen can be estimated √ as: τs (t) = 2 5E0 A0 ε t (t)/(5As ), τ s ( t ) = 2 5E0 A0ε t t (5 As ) , γ = Pd /t D ,
()
(3) (3) (4)
, ), γloc.γ ==PP dd/ (t3t DM
(5) (4)
γ loc. = Pd (3tM ) ,
(5)
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γ.
= v (2t ) ,
(6) (6)
loc. γloc. = v/(2tMM ),
where specimen, and and ttD and tM are the designed width of where A Ass is is the the initial initial cross-sectional cross-sectional area area of of the the specimen, D and tM are the designed width of the shear region (approximately 1 mm, dashed circle shown in Figure the shear region (approximately 1 mm, dashed circle shown in Figure 1) 1) and and measured measured shear shear band band width, respectively. width, respectively. The The shear shear stress stress can can be be converted converted into into normal normal stress stress (σ) (σ) as: as:
σ = 2τ .
(7) σ = 2τ. (7) The duration of shear deformation can be determined directly from the experimental data of the SHPBThe test, as shown in Figure 2a. The shear is approximately 100 data μs for duration of shear deformation can bedeformation determined duration directly from the experimental of the the specimen punching of 1.1deformation mm. The shear stressisversus punching 100 depth SHPB test,deformed as shownatina Figure 2a. depth The shear duration approximately µs curves for the at all punching depths showndepth in Figure where all of stress the curves oscillations due to specimen deformed at aare punching of 1.12b, mm. The shear versusexhibit punching depth curves at reflection of waves at the specimen surfaces and stopper rings. In addition, these curves show a all punching depths are shown in Figure 2b, where all of the curves exhibit oscillations due to reflection plateau foratdifferent punching depths, a sharp increase in shear stress when the steel stopper of waves the specimen surfaces and and stopper rings. In addition, these curves show a plateau for ring is contacted. is interesting to note that in theshear flowstress stresses arethe almost a constant different different punchingItdepths, and a sharp increase when steel stopper ringfor is contacted. punching depths to approximately 600 MPa, indicating that the flow stress of Ti-55511 It is interesting to and noteare thatequal the flow stresses are almost a constant for different punching depths and are alloy of 600 the punching depth.that Therefore, corresponding normal stress of Ti-55511 equalistoindependent approximately MPa, indicating the flowthe stress of Ti-55511 alloy is independent of the alloy can be taken as 1200 MPa. However, in our previous work, the normal stress of Ti-55511 punching depth. Therefore, the corresponding normal stress of Ti-55511 alloy can be taken as 1200alloy MPa. is approximately 1500 MPawork, for cylindrical specimens under dynamic [23]. Hence, However, in our previous the normal stress of Ti-55511 alloy iscompression approximately 1500 MPathe for corresponding normalunder stressdynamic in HS specimens is about 300 MPa than thatnormal in the stress cylindrical cylindrical specimens compression [23]. Hence, the lower corresponding in HS specimen. observed discrepancy attributed to the geometrical imperfection of HS specimens The is about 300 MPa lower thanmay that be in the cylindrical specimen. The observed discrepancy specimens. may be attributed to the geometrical imperfection of HS specimens. pd = 1.1 mm
Shear stress (MPa)
1000
1200
a)
Initiation of shear deformation
1000
Termination of shear deformation by stopper ring
800
600
400
Shear deformation duration (ca 100μs)
200
0
Without stopper ring pd = 1.1
b)
pd = 1 pd = 0.9
Shear stress (MPa)
1200
800
pd = 0.8 pd = 0.7
600
400
200
0
50
100
Time (μs)
150
0 0.0
0.5
1.0
1.5
Punching depth (mm)
Figure Figure 2. 2. (a) (a) Shear Shear stress stress vs vs time time for for the the HS HS sample sample deformed deformed at at aa punching punching depth depth of of 1.1 1.1 mm. mm. A A time time window of approximately approximately100 100µsμs indicating period during shear deformation; (b) shear window of indicating thethe period during shear bandband deformation; (b) shear stress stress vs different prescribed punching depths. upturn of when the curves when prescribed vs different prescribed punching depths. Notice theNotice upturnthe of the curves prescribed displacement displacement is reached. is reached.
3.2. 3.2. Microstructural Microstructural Characterization Characterization A typical SEM SEMmicrograph micrographof of undeformed specimen is depicted in Figure 3a. A A typical an an undeformed specimen is depicted in Figure 3a. A higherhigher-magnification TEM micrograph of the structure of β-transformation (matrix) in magnification TEM micrograph of the structure of β-transformation (matrix) is shown is in shown Figure 3b, Figure 3b, in which many thinner platelet α-phases can be observed. As shown in Figure 3, the initial in which many thinner platelet α-phases can be observed. As shown in Figure 3, the initial microstructure structure of of β-transformation β-transformation (matrix) microstructure of of Ti-55511 Ti-55511 alloy alloy consists consists of of the the structure (matrix) and and α-phase α-phase (platelet α and equiaxed α), and the size of equaxied α is approximately 4 μm. (platelet α and equiaxed α), and the size of equaxied α is approximately 4 µm.
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Figure 3. Initial microstructure of Ti-55511 alloy; (a) SEM micrograph and (b) TEM micrograph of Figure 3. Initial microstructure microstructure of Ti-55511 alloy; (a) SEM micrograph and (b) TEM micrograph of Figure 3. of Initial structure β-transformation. of Ti-55511 alloy; (a) SEM micrograph and (b) TEM micrograph of structure structure of of β-transformation. β-transformation.
Typical low-magnification optical micrographs of the well-developed localized shear bands are Typical low-magnification Typical low-magnification of the well-developed localized shear bands shown in Figure 4. Figure 4b–doptical are themicrographs higher magnifications of region “A” shown in Figure 4a. are As in Figure 4. Figure 4b–d are the higher magnifications of region “A” shown in Figure 4a. As shown Figure 4. Figure 4b–d are the higher magnifications of region “A” shown in Figure 4a. shown in Figure 4, the values of shear band width range from 20–28 μm. Typical SEM micrographs shown in Figure 4, the values of of shear width from μm. SEM As shown in Figure 4, the values band widthrange range from20–28 20–28 µm.Typical Typical SEMofmicrographs of the shear-deformation region inshear theband HS specimen deformed at a punching depth 0.8 mm are the shear-deformation region in the HS specimen deformed at a punching depth 0.8are mm are of the shear-deformation region in the HS specimen deformed at a punching depth of 0.8ofmm show show in Figure 5. Figure 5a shows an ASB with an associated crack, and a higher-magnification show in Figure 5. Figure 5a shows an ASB with an associated crack, and a higher-magnification in Figure 5. Figure 5a shows an ASB with an associated crack, and a higher-magnification micrograph micrograph of region “A” in Figure 5a is shown in Figure 5b. micrograph in shown Figure in 5aFigure is shown of region “A”ofinregion Figure“A” 5a is 5b. in Figure 5b.
Figure 4. Cont.
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Figure 4. specimens Figure 4. 4. Typical Typical optical optical micrographs micrographs of of shear-deformation shear-deformation regions regions in in HS HS specimens specimens deformed deformed at at d = 1.0 mm; (c) Pd = 0.9 mm; (d) Pd = 0.7 mm. different punching depths (a) without stopper ring; (b) P 1.0 mm; mm; (c) (c) PPdd = 0.9 mm; (d) Pdd ==0.7 different punching punching depths depths(a) (a)without withoutstopper stopperring; ring;(b) (b)PPdd== 1.0 different 0.7 mm. mm.
Figure Figure 5. 5. Typical Typical SEM SEM micrographs micrographs of of shear-deformation shear-deformation regions regions in in HS HS specimens specimens deformed deformed at at P Pdd == Figure 5.(a)Typical SEM micrographs of shear-deformation regions in HS specimens deformed at 0.8 mm: a shear band and an associated crack and (b) higher magnification of A in Figure 5a. 0.8 mm: (a) a shear band and an associated crack and (b) higher magnification of A in Figure 5a. Pd = 0.8 mm: (a) a shear band and an associated crack and (b) higher magnification of A in Figure 5a.
As As shown shown in in Figures Figures 44 and and 5, 5, α-phases α-phases adjacent adjacent to to the the ASB ASB are are elongated elongated along along the the shear shear direction due to the strong shear deformation. The size of elongated “equaxied” α-phases along As shown in Figures 4 and 5, α-phases adjacent to the ASB are elongated along the shear direction direction due to the strong shear deformation. The size of elongated “equaxied” α-phases along the the shear is 5–6 than the size 44 μm undeformed due the strong shear deformation. size elongated α-phases along specimen the shear sheartodirection direction is about about 5–6 μm, μm, larger largerThe than theofinitial initial size of of“equaxied” μm for for the the undeformed specimen (Figure With further the elongated up structures within direction is about µm,deformation, larger than the initial size ofα-phases 4 µm for break the undeformed specimen (Figure 2a). (Figure 2a). 2a). With 5–6 further deformation, the elongated α-phases break up into into small small structures within or to shear Moreover, aa very distinctive boundary separates the shear from With further deformation, elongated α-phases break up into small structures or close to the or close close to the the shear band. band.the Moreover, very distinctive boundary separates thewithin shear band band from the surrounding deformed structures. It should be noted that although the cracks extend into the shear band. Moreover, a very distinctive boundary separates the shear band from the surrounding surrounding deformed structures. It should be noted that although the cracks extend into the shear shear band extent almost cracks the band/matrix deformed structures. should 4d), be noted thatall the cracksat into the shear bandinterface. to some band to to some some extentIt(Figure (Figure 4d), almost allalthough cracks occurred occurred atextend the shear shear band/matrix interface. Similar phenomena have been observed in Ti-55511 alloy [16,28,29]. extent (Figure 4d), almost all cracks occurred at the shear band/matrix interface. Similar phenomena Similar phenomena have been observed in Ti-55511 alloy [16,28,29]. of for loading condition have The beenwidth observed in Ti-55511 [16,28,29]. The width of ASB ASB for each eachalloy loading condition is is measured measured and and plotted plotted in in Figure Figure 6. 6. It It is is shown shown that the width of ASB increases with the increase of global shear strain (punching depth), and The width of ASB for each loading condition is measured and plotted in Figure 6. It is shown that the width of ASB increases with the increase of global shear strain (punching depth), and tends tends to at 30 μm. The measured widths are compared with values that the width of ASB increases of global shear (punching depth), andpredicted tends to to saturate saturate at approximately approximately 30with μm.the Theincrease measured widths are strain compared with the the values predicted using proposed by Bai et and and will discussed in saturate at equation approximately 30 µm. are compared withwhich the values predicted using using the the equation proposed by The Bai measured et al. al. [30] [30] widths and Dodd Dodd and Bai Bai [13], [13], which will be be discussed in Section 3.3. the equation Section 3.3. proposed by Bai et al. [30] and Dodd and Bai [13], which will be discussed in Section 3.3. Combined microstructures shown shown in in Figures Figures 444 and and 5, Combined with with our our previous previous work work [16,29] [16,29] and and the the microstructures microstructures shown in Figures and 5, sequence of the microstructural evolution within an ASB for Ti-55511 alloy can be summarized, the sequence of the microstructural evolution within an ASB for Ti-55511 alloy can be summarized, and the sequence of the microstructural evolution within an ASB for Ti-55511 alloy can be summarized, and 77 is the representation. As shown Figure 7a, an due Figure 7 is the schematic representation. As shown Figurein an ASB dueforms to the occurrence and Figure Figure is the schematic schematic representation. As in shown in7a, Figure 7a,forms an ASB ASB forms due to to the the occurrence of severe strain concentration in the shear region, and the grains or phases near the of severe strain concentration in the shear region, and the grains or phases near the ASB are rotated occurrence of severe strain concentration in the shear region, and the grains or phases near the ASB ASB are and elongated along the direction (shown in 44 and 5). microcracks and elongated the shear direction (shown in Figures 4 and 5). Then, microcracks nucleated are rotated rotated andalong elongated along the shear shear direction (shown in Figures Figures and 5). Then, Then,are microcracks are nucleated at the shear band/matrix interface (Figure 7b), and adjoining microcracks coalesce to at the shear band/matrix interface (Figure 7b), and adjoining microcracks coalesce to a bigger are nucleated at the shear band/matrix interface (Figure 7b), and adjoining microcracks coalescecrack to aa bigger crack (Figure 7c). With further deformation, the crack propagates along two ways. One is that (Figure 7c). With further deformation, the crack propagates along two ways. One is that the crack bigger crack (Figure 7c). With further deformation, the crack propagates along two ways. One is that the along the interface 7d) failure or propagates along the shear interface (Figure 7d)(Figure up to failure 7g). the crack crack propagates propagates along band/matrix the shear shear band/matrix band/matrix interface (Figure 7d) up uporto tofracture failure (Figure or fracture fracture (Figure 7g). The other one is that the crack extends into the ASB and propagates along the shear (Figure 7g). The other one is that the crack extends into the ASB and propagates along the shear band/matrix band/matrix interface interface (Figure (Figure 7e,f) 7e,f) up up to to failure failure or or fracture fracture (Figure (Figure 7h). 7h). It It is is interesting interesting to to note note that that
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The other one is thatPEER the crack extends into the ASB and propagates along the shear band/matrix Materials 7 7ofof1212 Materials2018, 2018,11, 11,x xFOR FOR PEERREVIEW REVIEW interface (Figure 7e,f) up to failure or fracture (Figure 7h). It is interesting to note that the features of ASB evolution inASB Ti-55511 alloy in are similar those of similar adhesive “adhesive fracture” the evolution alloy are those adhesive fracture. Hence, thefeatures featuresofof ASB evolution inTi-55511 Ti-55511to alloy are similartotofracture. thoseofofHence, adhesive fracture. Hence, can be identified as the dynamic failure mechanism for Ti-55511 alloy [29]. “adhesive fracture” can be identified as the dynamic failure mechanism for Ti-55511 alloy [29]. “adhesive fracture” can be identified as the dynamic failure mechanism for Ti-55511 alloy [29]. 30 30
Measured values Measured values
Widths of ASB (μm) Widths of ASB (μm)
28 28 26 26 24 24 22 22 20 20 0.3 0.3
0.4 0.4
0.5 0.5
Global shear strain Global shear strain
0.6 0.6
0.7 0.7
Figure 6.6.Widths ofofshear shear bands asasaa afunction function ofofglobal global shear strain. Figure6. Widthsof shearbands bandsas functionof globalshear shearstrain. strain. Figure Widths
Figure 7.7.Schematic Schematic representation the sequence microstructural evolution within an Figure representation ofofof the sequence ofof the microstructural evolution within an ASB for Figure7. Schematic representation the sequence ofthe the microstructural evolution within anASB ASB for Ti-55511 alloy. (a): ASB formation; (b): microcracks formation (red points at the shear Ti-55511 alloy. (a): ASB formation; (b): microcracks formation (red points at the shear band/matrix for Ti-55511 alloy. (a): ASB formation; (b): microcracks formation (red points at the shear band/matrix microcracks (d): propagation along the interface); (c):interface); adjoining(c): microcracks (d): coalesce; crack propagation the shear band/matrix band/matrix interface); (c):adjoining adjoiningcoalesce; microcracks coalesce; (d):crack crackalong propagation along theshear shear band/matrix interface; (e,f): crack propagated into the ASB; (g,h): ultimate fracture. interface; (e,f):interface; crack propagated into the ASB; (g,h): ultimate fracture. band/matrix (e,f): crack propagated into the ASB; (g,h): ultimate fracture.
The microstructure within and/or ASB was characterized by TEM, and characteristic Themicrostructure microstructurewithin withinand/or and/orclose closeto ASBwas wascharacterized characterizedby byTEM, TEM,and andcharacteristic characteristic The close totoASB microstructures of the shear region at different punching depths are shown in Figure 8. As shown inin microstructuresofofthe theshear shearregion regionatatdifferent differentpunching punchingdepths depthsare areshown shownininFigure Figure8.8.As Asshown shownin microstructures Figure 2b, the initial microstructure of undeformed Ti-55511 alloy shows low dislocation density in Figure2b, 2b,the the initial microstructure of undeformed Ti-55511 alloy shows dislocation density Figure initial microstructure of undeformed Ti-55511 alloy shows low low dislocation density in thein the Compared with the ofof Ti-55511 alloy, asas shear the crystal. crystal. Compared with the initial initial microstructure microstructure Ti-55511 alloy,deformation shear deformation deformation crystal. Compared with the initial microstructure of Ti-55511 alloy, as shear proceeds, proceeds, planar parallel dislocations and dislocation dipoles can be observed (see Figure 8a). Due proceeds, planar parallel dislocations and dislocation dipoles can be observed (see Figure 8a). Duetoto planar parallel dislocations and dislocation dipoles can be observed (see Figure 8a). Due to the motion the motion of dislocations along the shear direction, bamboo incidental dislocation boundaries form motion of dislocations along the shear direction, bamboodislocation incidental boundaries dislocation boundaries ofthe dislocations along the shear direction, bamboo incidental form when form the when punching depth increased to 0.8 (see Figure 8b). the punching depth whenthe thedepth punching depthis increased 0.8mm mm Figure 8b).When When theis punching depthisis punching is increased tois0.8 mm (seeto Figure 8b). (see When the punching depth further increased further increased toto0.9 cell structures form from various slip begin increased 0.9mm, mm, cellas structures formasasthe thedislocations dislocations various slipsystems systems tofurther 0.9 mm, cell structures form the dislocations from various slipfrom systems begin to tangle begin and tototangle and pile up (see Figure 8c,d). These small areas or cells, outlined by broad boundaries, pile 8c,d). up (seeThese Figure 8c,d).areas These or cells, outlined by broadexhibit boundaries, pile tangle up (seeand Figure small or small cells, areas outlined by broad boundaries, very exhibit exhibitvery veryfew fewororno noindividual individualdislocations. dislocations.Moreover, Moreover,aadislocation dislocationpile-up pile-upgroup groupand andstacking stacking fault can be observed easily. The break-up of elongated cells can also be observed in fault can be observed easily. The break-up of elongated cells can also be observed inFigure Figure8d 8d (marked (markedby bythe thedotted dottedcircle). circle).The Thetridimensional tridimensionalshape shapeofofthe theelongated elongatedcells cellsisisexpected expectedtotobe beaa “pancake”, “pancake”,since sincethe theobservation observationwas wasmade madeon onaaplane planethat thatwas wasparallel paralleltotothe theshear sheardirection. direction.AA
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few or no individual dislocations. Moreover, a dislocation pile-up group and stacking fault can be observed easily. The break-up of elongated cells can also be observed in Figure 8d (marked by the dotted circle). The tridimensional shape of the elongated cells is expected to be a “pancake”, since the observation was made on a plane that was parallel to the shear direction. A similar result has been Materials 2018, 11, x FOR PEER REVIEW 8 of 12 reported by Meyers et al. [7]. With further deformation (Pd = 1.0 mm), some grains and/or phases are broken into withby a size of approximately 60–90deformation nm. Apparently, similar up result hassubgrains been reported Meyers et al. [7]. With further (Pd = 1.0these mm), subgrains some are essentially freephases of dislocations. one shot test (sample forced sheared by split Hopkinson grains and/or are broken For up into subgrains with a size of approximately 60–90 nm. Apparently, these subgrains are essentially freesevere of dislocations. For one shotthe testadjoining (sample forced pressure bar without stopper ring), due to the shear deformation, subgrains split Hopkinson pressure bar without stopper due to the severeenergy shear deformation, with sheared a small by misorientation between them will attempt toring), lower their surface by rotating into the adjoining subgrains with athe small misorientation between will attempt to lowerDue theirto the coincidence, thereby eliminating low-angle boundary that them separates them [27,31]. surface energy by rotating into coincidence, thereby eliminating the low-angle boundary that rotating and coalescence of adjoining subgrains, the nanograins with a size of about 6 nm can be separates them [27,31]. Due to the rotating and coalescence of adjoining subgrains, the nanograins observed (see Figure 8f). The selected area-diffraction pattern shows incomplete rings, which indicate with a size of about 6 nm can be observed (see Figure 8f). The selected area-diffraction pattern shows the presence of dynamic recrystallization (DRX, marked by arrows). This is in accordance with the incomplete rings, which indicate the presence of dynamic recrystallization (DRX, marked by resultarrows). reported byisRittel et al. [9].with the result reported by Rittel et al. [9]. This in accordance
Figure 8. TEM micrographs of shear-deformation regions in HS specimens deformed at different
Figure 8. TEM micrographs shear-deformation in HS specimens deformed at different (b) Pd = 0.8 mm, (c)regions Pd = 0.9 mm, (d) P d = 0.9 mm, (e) Pd = 1.0 mm and punching depths: (a) Pd = 0.7ofmm, punching depths: (a) P = 0.7 mm, (b) P = 0.8 mm, (c) P = 0.9 mm, (d) P = 0.9 mm, (e) Pd = 1.0 mm d d d d (f) without stopper ring. and (f) without stopper ring. Relying on the aforementioned analysis, the difference of the microstructures within the ASB of Ti-55511 alloy is dependent on the punching depth/plastic deformation. The sequence of plastic deformations taken place in the shear region can be summarized as: (a) occurrence of parallel planar
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Relying on the aforementioned analysis, the difference of the microstructures within the ASB of Ti-55511 alloy is dependent on the punching depth/plastic deformation. The sequence of plastic deformations taken place in the shear region can be summarized as: (a) occurrence of parallel planar dislocations; (b) formation of bamboo incidental dislocation boundaries; (c) formation of cells and/or elongated cells; (d) formation of subgrains; and (e) formation of nanograins. Based on the criterion proposed by Derby [32] and Takeuchi and Argon [33], the recrystallized grain size can be estimated as: λ = KbG/σ, (8) with 1 < K < 15. G, σ and b are the shear modulus, applied stress and Burgers vector, respectively. For Ti-55511 alloy, G and b are 40 GPa and 2.3 × 10−10 m, respectively. σ is about 1.2 GPa. Thus, the estimated DRX size of Ti-55511 alloy ranges from 6–90 nm, which agrees well with our experimental observations. Based on the adiabatic assumption, a large portion of the plastic work within a shear band is converted into heat to raise the local temperature [34]. The maximum temperature during the forced shear tests can be estimated as: R β τdγ + T0 , (9) T = ∆T + T0 = ρC where ρ is the mass density, C is the specific heat, T0 is the ambient temperature and β is the fraction of plastic work converted to heat, which is taken as 0.9. For Ti-55511 alloy, ρ and C are 4625 kg/m3 and 523 J/(kg K), respectively. Here, T0 = 293 K. The estimated maximum temperature in our tests is approximately 573 K. Such a temperature is much lower than those of α→ β phase transformation (approximately 1163 K) and dynamic recrystallization (0.4 Tm [25], approximately 760 K). Hence, this observation indicates that thermal softening has a very minor effect on the onset of ASB and subgrain/nanograin formation. Similar findings have also been reported by Rittel et al. [9] and Clos et al. [35]. Therefore, the nucleation mechanism for DRX can be assumed as strain-induced boundary migration and subgrain rotation and coalescence. Similar phenomena have been reported in copper [25,27] and TA2 [7]. 3.3. Estimation of ASB Width The width of ASB has been satisfactorily predicted with perturbation analyses [13,14]. The contribution of heat conduction to the thickness of a shear band was included in these analyses [30]. A very simple estimation of the ASB width has been given by Bai et al. [30] and Dodd and Bai [2,13,14], s δ=2
λTmax , . βτ γloc
(10)
where δ is the shear band width, and λ and Tmax are the thermal conductivity and maximum temperature within the shear band, respectively. For Ti-55511 alloy, λ is equal to 9.21 W/(m K). The applied shear stress of Ti-55511 alloy in HS specimens is estimated as a constant of 600 MPa. p Then, the width of ASB can be considered as a linear function of Tmax /γloc . The calculated width of ASB and the ratio of the calculated and measured pwidths of ASB for each test are listed in Table 2. Figure 9 shows the width of ASB plotted against Tmax /γloc . It is shown that the widths of ASB predicted using Equation (9) are much smaller than the experimental results.
experimental result in our previous work, in which the measured ASB width for Ti-55511 alloy is about 6–9 μm in compression tests of cylindrical specimens [23]. Meyers et al. [7] and Chen et al. [15] calculated the ASB width for different materials in HS specimens, and gave different results. A three-fold difference between experimentally observed and calculated results was observed in TA2 by Meyers Materials 2018, et 11, al., 839 while Chen et al. reported that the experimentally observed width was slightly 10 of 12 higher than that calculated for tantalum. In the present study, the measured widths of ASB are about two-times larger than the calculated results. Though Wang et al. [28] did not calculate the thickness Summary of the global shear strain, local shear strain rate, maximum temperature and of theTable ASB2.using Equation (9), in their work, the calculated width of ASB was approximately 1/3 of ASB width. the measured one (H4 sample). Hence, for Ti-55511 alloy, the measured thickness of ASB has about a . three-fold difference from the calculated results. Therefore, the calculation of ASB width for HS Pd /mm tM /µm tD /mm γ γloc T max /K δ/µm δ/tM v/ms−1 flloc /s−1 specimens can be modified as: 5 0.7 0.8 0.9 1 1.1 Without stopper ring
23.8 23.7 23.7 23.7 23.5 23.8
20.1 23.2 25.5 27.3 27.9 28.2
where k is the coefficient.
1.01 1.03 1.02 δM 1.01 1.04 1.02
=
0.693 34.83 0.777 λTmax34.48 35.29 , k 20.882 0.990τγ 36.63 loc 1.058 39.43 1.196 46.10
5.92 × 10 5.11 × 105 4.65 × 105 4.34 × 105 4.21 × 105 4.22 × 105
454 467 494 504 532 573
6.86 7.49 8.08 8.44 8.81 9.13
2.93 3.10 3.16 (11) 3.23 3.17 3.09
Thickness (μm)
30
20 Experimental results Calculated Modified 10
0 2.5x10-2
3.0x10-2
3.5x10-2
(Tmax/γloc)(1/2)
Figure 9. 9. Width Width of of ASB ASB in in Ti-55511 Ti-55511 alloy alloy (HS (HS specimens) specimens) as as aa function function of of the the maximum maximum temperature temperature Figure and local shear strain rate. The theoretical predictions using the original Formula (10) and the and local shear strain rate. The theoretical predictions using the original Formula (10) and the modified modified one (11) are given for comparison. one (11) are given for comparison.
Relying on the aforementioned analysis, the values of k for TA2, tantalum and Ti-55511 alloy It should be pointed out that the width of ASB predicted using Equation (9) agrees well with are 1/3, 1 and 3, respectively. The discrepancy may be attributed to the material itself. Further the experimental result in our previous work, in which the measured ASB width for Ti-55511 investigation is needed to clarify this issue. It should be noted that the result obtained in the present alloy is about 6–9 µm in compression tests of cylindrical specimens [23]. Meyers et al. [7] and study cannot be generalized to other metallic materials until further tests are carried out. Chen et al. [15] calculated the ASB width for different materials in HS specimens, and gave different results. A three-fold difference between experimentally observed and calculated results was observed 4. Conclusions in TA2 by Meyers et al., while Chen et al. reported that the experimentally observed width was slightly A than seriesthat of dynamic shear tests were carried out on alloy at 293 by are means of higher calculatedforced for tantalum. In the present study, theTi-55511 measured widths of K ASB about the SHPB larger technique HS specimens with et the technique, and the two-times thanusing the calculated results.combined Though Wang al.“strain-frozen” [28] did not calculate the thickness microstructure of the localized shear region was examined. According to the experimental findings, of the ASB using Equation (9), in their work, the calculated width of ASB was approximately 1/3 of the following can beHence, drawn:for Ti-55511 alloy, the measured thickness of ASB has about the measured conclusions one (H4 sample). a(a)three-fold difference thespecimens calculated of results. Therefore, the calculation of of ASB width HS The flow stress infrom the HS Ti-55511 alloy remains a constant about 600for MPa, specimens be modified as: and is can independent of punching depth. s
(b) The width of the shear band increases with λT themax increase of punching depth and tends to δM = 2k , (11) saturate at 30 μm, and the estimation of the ASBτγ width in HS specimens has been modified. loc
where k is the coefficient. Relying on the aforementioned analysis, the values of k for TA2, tantalum and Ti-55511 alloy are 1/3, 1 and 3, respectively. The discrepancy may be attributed to the material itself. Further investigation is needed to clarify this issue. It should be noted that the result obtained in the present study cannot be generalized to other metallic materials until further tests are carried out. 4. Conclusions A series of dynamic forced shear tests were carried out on Ti-55511 alloy at 293 K by means of the SHPB technique using HS specimens combined with the “strain-frozen” technique, and the
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microstructure of the localized shear region was examined. According to the experimental findings, the following conclusions can be drawn: (a) (b) (c) (d)
The flow stress in the HS specimens of Ti-55511 alloy remains a constant of about 600 MPa, and is independent of punching depth. The width of the shear band increases with the increase of punching depth and tends to saturate at 30 µm, and the estimation of the ASB width in HS specimens has been modified. Thermal softening has a minor effect on the onset of ASB and DRX formation, and the nucleation mechanism for DRX is strain-induced boundary migration and subgrain rotation and coalescence. For Ti-55511 alloy, the features of microstructural evolution in high-strain-rate loading situations are similar to those of adhesive fracture, and the concept of adhesive fracture is proposed as the dynamic failure mechanism for Ti-55511 alloy.
Author Contributions: C.R. and P.C. conceived and designed the experiments; C.R. and Z.S. conducted the forced shear tests; C.R., J.L. and W.Z. analyzed the data; and Chun Ran and P.C. worte the paper. Acknowledgments: This research was funded by the National Natural Science Foundation of China (Grant Nos. 11472054, 11521062), and the State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, China, with Grant No. ZDKT18-01. D. Rittel at Technion Israel institute of Technology is kindly acknowledged for his valuable discussion and suggestions. Conflicts of Interest: The authors declare no conflict of interest.
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