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Effect of grain size on twinning behavior in Ti–2Al–2.5Zr alloy fatigued at 77 K
Materials Science and Engineering A 542 (2012) 1–7
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Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Effect of grain size on twinning behavior in Ti–2Al–2.5Zr alloy fatigued at 77 K H. Wang a,b , Q.Y. Sun a,∗ , L. Xiao a , J. Sun a a b
State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China Tubular Goods Research Institute of China National Petroleum Corporation, Xi’an 710065, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 29 July 2011 Received in revised form 9 January 2012 Accepted 24 January 2012 Available online 17 February 2012 Keywords: Low-cycle fatigue Deformation structure Twins Stacking faults Ti–2Al–2.5Zr
a b s t r a c t The low-cycle fatigue (LCF) behavior and plastic deformation mechanism were studied in Ti–2Al–2.5Zr alloy with different grain sizes of 5, 40, and 100 m fatigued at 77 K. The results show that LCF life decreases as grain size increases. Microstructural observation with transmission electron microscopy (TEM) reveals that the deformation structure evolves from twins to stacking faults as grain size increases. Deformation twinning is prevalent in the 5 m fine-grained sample. However, stacking faults with welldefined fringes were observed to occur inside deformation twins, which were separated by ribbon in coarse-grained samples of 40 and 100 m. This type of stacking faults has an implication for activating of extended dislocations during cyclic deformation. The plastic deformation mode transition could be attributed to the growing of localized stress concentration with increasing of grain size. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Twin plays a significant role in maintaining homogeneous plastic deformation in hexagonal close-packed (hcp) metals owing to their limited number of slip systems [1,2]. Up to date, twinning systems {1 1 2¯ 2}1¯ 1¯ 2 3, {1 1 2¯ 4}2¯ 2¯ 4 3 and {1 0 1¯ 1}1¯ 0 1 2 have been reported in Ti alloys [3–6]. The other possible twinning systems include {1 0 1¯ 2}, {1 1 2¯ 1} and {1 1 2¯ 3} [7]. A variety of nucleation models of twinning have been proposed depending on stacking fault energy (SFE) of materials. These models can be mainly categorized into three groups: (I) pole mechanism, which produces perfect twins without SF [8,9]; (II) models based on deviation processes, which produce intrinsic stacking fault together with the nucleation of Frank [10] or stair-rod [11–13] sessile dislocations; (III) models based on the interactions between extrinsic stacking faults [13–15]. It is well established that a slip on {1 0 1¯ 0} prism plane is the most active deformation mode in Ti. The other possible slip systems include {1 0 1¯ 1} and {1 0 2¯ 2} pyramidal slips and (0 0 0 2) basal slip. A total of only four independent deformation modes are possible by prism, basal and pyramidal slips with a Burgers vector. When a slip system with a c+ a Burgers vector is operative, this alone provides five independent deformation modes. Therefore, c+ a pyramidal slip and twinning play an important role in Ti alloys subjected to a large amount plastic deformation. Using molecular dynamic simulations (MDS), Li et al. [16] studied pyramidal slip
∗ Corresponding author. Tel.: +86 29 82668614; fax: +86 29 82663453. E-mail address: [email protected] (Q.Y. Sun). 0921-5093/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2012.01.106
in single crystal Mg, and reported that pyramidal slip was actually mediated on the {1 0 1¯ 1} plane by two independent dislocations. When these two dislocation slips combined on the surface, c+ a displacement was created. In the absence of the other dislocations, the first incomplete dislocation can leave behind a wide stacking fault on the {1 0 1¯ 1} twinning plane. We [17] investigated the effect of grain size on deformation mode in hcp titanium alloy and found a transition of plastic deformation mode from twinning together with slip to slip alone as the grain size decreased from 40 to 5 m at room temperature (RT). Deformation twins were significantly restricted at RT as grain size decreased from tens of micrometers to several microns. However, when those fine-grained samples were fatigued at 77 K, twinning was observed to be activated and became one of dominant plastic deformation modes. Consequently, the higher ductility and the longer LCF life were exhibited at 77 K than those at RT. The hcp metals have a complicated plastic deformation mode including dislocation slip with different Burgers vectors and twinning with different deformation directions and systems [13]. It is generally believed that stacking faults appear on the basal plane, and non-basal stacking faults can not form in hcp crystals because of their high SFE [16]. The stacking faults in hcp metals attract much less attention than those in fcc and bcc metals. Li et al. [18] have investigated the stacking faults and their interaction with pyramidal dislocations in plastically deformed polycrystalline pure Mg, and reported that the stacking faults consisted of well-defined fringes and streaking. The basal stacking faults were observed to be decorated by a large number of dark speckles, which were proposed to be created due to the interaction between pyramidal slip dislocations with both c and a components, themselves. The objective
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H. Wang et al. / Materials Science and Engineering A 542 (2012) 1–7
Fig. 1. Metallograph of Ti–2Al–2.5Zr samples with different grain sizes: (a) 5 m; (b) 40 m and (c) 100 m.
of this work is to study the effect of grain size on LCF behavior and to ascertain the relationship between planar slip of extended dislocations and twinning in hcp titanium alloy at low temperature, when twin plays a dominant role. 2. Experimental The material used in the present work is a commercial grade Ti–2Al–2.5Zr, which is a typical single-phase alpha titanium alloy. The initial condition of material was an extruded bar of 35 mm in diameter. These bars were further extruded to 14 mm in diameter in a hydraulic test frame so as to refine the grain size. The rods with 5 m of fine grains were produced at an extrusion temperature of about 830 ◦ C. Meanwhile, some of extruded rods were further annealed at 800 ◦ C for 2 h and 16 h in order to promote the grain growth, respectively. The diameter of coarse grains was measured to be 40 and 100 m, according to an evaluation of linear intercept method. Both fine and coarse grains were equiaxed structures, as shown in Fig. 1(a)–(c). These rods were then machined into tension and fatigue samples with 13 mm in gauge length and 7.5 mm in diameter. Both tension and symmetrical push-pull fatigue tests were performed on an INSTRON 1141 fatigue testing system. The strain rate was 6.67 × 10−4 s−1 for tension test. Symmetrical push-pull fatigue tests were performed under total displacement control in liquid nitrogen environment at 77 K. A triangular loading waveform was used with a frequency of 0.25 Hz. Double fatigue specimens were tested each strain amplitude. The stress–strain hysteresis loops were used to determine the cyclic peak stress responses and plastic strain amplitudes as a function of the number of cycles.
Specimens were soaked into a liquid nitrogen bath during testing. Tests did not carry out until the sample had been stabilized at a designed temperature of 77 K for 1 h. The detailed information about LCF experiment at 77 K had been described elsewhere [17]. After failure, deformed specimens were spark-cut within gauge. Thin foils for transmission electron microscopy (TEM) were prepared from 3-mm discs cut along cross section within gauge and thinned with a twin-jet. The fatigue dislocation substructures were observed using a JEM-200CX transmission electron microscope operated at 200 kV. 3. Results 3.1. Tensile and cyclic deformation behavior Tensile stress–strain curves of Ti–2Al–2.5Zr alloy samples with different grain sizes at 77 K are shown in Fig. 2(a). The results show that the 5 m fine-grained sample has an obvious higher strength but lower ductility than those of the 40 and 100 m coarse-grained samples. On a close examination, the coarse-grained of 100 m sample has a higher ultimate tensile strength (UTS) than that of 40 m sample due to its high strain hardening rate, even though it has lower yield stress. Yield stress decreases, while the ductility increases, as grain size increases from 40 to 100 m. Fig. 2(b) shows the effect of grain size on yield stress and elongation of Ti–2Al–2.5Zr alloy. It is demonstrated that grain size has an obvious effect on both strength and ductility. The yield stress decreases but the elongation ductility enhances as the grain size increases from 5 to 100 m. The detailed mechanical property data were summarized in Table 1. The relation between fatigue life and cyclic total strain amplitude in Ti–2Al–2.5Zr is plotted in Fig. 3. It is revealed that the
Table 1 Tensile properties of Ti–2Al–2.5Zr alloy with different grain sizes at 77 K. Grain size (m)
Yield stress (MPa)
Ultimate tensile strength (MPa)
Elongation (%)
Reduction in area (%)
Elastic module (GPa)
100 40 5
714 760 961
964 913 1116
55.0 48.8 24.3
36.2 65.5 53.3
136.6 138.2 143.6
H. Wang et al. / Materials Science and Engineering A 542 (2012) 1–7
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Fig. 2. Tensile property curves of Ti–2Al–2.5Zr with different grain sizes at 77 K. (a) Stress–strain curves and (b) yield stress/elongation vs. grain size curves.
curve of fine-grained samples of 5 m lies over that of coarsegrained samples of 40 m. Furthermore, the lifetimes of 40 m of samples are longer than those of 100 m of samples at the same strain amplitude. There is a similar linear rate of fatigue life curves between 5 m and 40 m grain samples. In comparison, the lower the cyclic total strain amplitude, the longer the LCF life is in samples with 40 m in comparison with 100 m samples. These results indicate that the fine-grained samples exhibit the longer LCF lives than those of coarse-grained samples, specifically at low cyclic strain amplitudes. 3.2. Deformation substructure 3.2.1. Twinning in fine-grained sample Deformation structures were examined in Ti–2Al–2.5Zr alloy with different grain sizes fatigued at 77 K. Fig. 4 shows a micrograph observed in sample with a grain size of 5 m fatigued at εt /2 = 2.0%. Twinning is a prevalent deformation mode. It was determined to be {1 0 1¯ 1}-type twin in the form of parallel-sides extending overall grain. Further examination showed that a streaking planar defect was produced along twin boundaries, as indicated by arrows in Fig. 4. 3.2.2. Twins and stacking faults in the coarse-grained sample of 40 m Fig. 5 shows a typical microstructure formed in the coarsegrained sample of 40 m fatigued at εt /2 = 2.0%. Deformed twins in the form of parallel-sides were also observed. Some high density of dislocations perpendicular to twin boundaries was formed
Fig. 3. Effect of grain size on the LCF life of Ti–2Al–2.5Zr at 77 K.
Fig. 4. Deformation twins formed in the fine-grained sample fatigued at 77 K (˜g = 1 0 1¯ 0; incident beam [1¯ 2 1¯ 1]).
inside these twins. The other dislocation lines aligned along twin boundaries were produced, as indicated by arrows in Fig. 5. The dislocation density inside twin is much higher than that outside one. This implies that twin boundaries (TBs) could block the moving of dislocations. When εt /2 = 4.5%, the streaking planar defects appeared inside deformation twins with parallel-sides, as shown in Fig. 6(a). On the basis of the contrast analysis with the weakbeam dark-field (WBDF) technique, the streaking planar defects accompanying with tangled dislocation occurred. Further analysis showed that these separated segments could be formed due to
Fig. 5. Deformed twins formed in the coarse-grained sample fatigued at 77 K (˜g = 1 0 1¯ 0; incident beam [1¯ 2 1¯ 1]).
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Fig. 6. Deformed twins formed in the coarse-grained samples (40 m) fatigued at 77 K: (a) bright-field image and (b) its corresponding dark-field image (˜g = 0 1¯ 1 3; incident beam [1¯ 2 1¯ 1]).
Fig. 7. Stacking faults formed inside deformed twins in coarse-grained sample fatigued at 77 K: (a) bright-field image and (b) its corresponding dark-field image, (˜g = 1 0 1¯ 0; incident beam [1¯ 2 1¯ 6]).
the intersecting among tangled dislocations, as shown in Fig. 6(b). Fig. 7 shows a set of bright-field and the weak-beam dark-field images of microstructural features inside twins. It is worth noting that several narrow fringes with dark/bright features together with streaking-like features occur inside twins, as indicated by arrows in Fig. 7(a). Some planar stacking faults were produced in the form of stair-like fringes, even though their contrast was weak, as indicated by arrows in Fig. 7(b). The similar stacking faults including long and short plates of precipitates and ribbons of stacking were observed in the solution-treated hcp Mg–Y–Zn alloys [19]. Stacking faults separated by a ribbon were observed both inside and outside twinning regions in the coarse-grained sample fatigued at εt /2 = 5.5%, as shown in Fig. 8(a). The ribbon became invisible but these stacking faults with alternative fringes were still distinct through titling the foil, as shown in Fig. 8(b). On a close examination, several mobile dislocation lines were observed to be emanated from these
stacking faults. This suggested that stacking faults could emit dislocation during cyclic deformation. Fig. 9 is a micrograph showing stacking faults formed inside and outside twinning regions, simultaneously. Stacking faults with a streak-like feature were observed inside a twin on the right of this micrograph, while stacking faults were separated by ribbon in the middle of this micrograph. In addition, the initiation of planar defects with dark/bright features was observed on the left of this micrograph. Some high density of dislocations accumulated around these initial stacking faults, indicating the nucleation of stacking faults related to the dislocation activity. 3.2.3. Stacking faults in the coarse-grained sample of 100 m Fig. 10 is a micrograph observed in the coarse-grained sample of 100 m fatigued at εt /2 = 2.5%. A large number of stacking faults with well-defined fringes emanated from the twin boundary, as indicated by arrows in Fig. 10. A few of straight deformation traces
Fig. 8. Stacking faults with fringes and an embedded ribbon in the coarse-grain sample fatigued at 77 K: (a) bright-field image and (b) dark-field image, (˜g = 0 1¯ 1 3; incident beam [1¯ 2 1¯ 1]).
H. Wang et al. / Materials Science and Engineering A 542 (2012) 1–7
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Fig. 9. Bright-field image showing stacking faults with features of streaks, stacking faults separated by ribbon and stacking faults inside twins in the coarse-grain sample fatigued at 77 K (˜g = 0 1¯ 1 3; incident beam [1¯ 2 1¯ 1]).
Fig. 12. Stacking faults inside twins in the sample with a grain size of 100 m fatigued at εt /2 = 4.5% (˜g = 1 0 1¯ 0; incident beam [1¯ 2 1¯ 6]).
Fig. 10. SFs with fringes formed in deformed twins in the coarse-grained samples of 100 m fatigued at 77 K (˜g = 0 1¯ 1 3; incident beam [1¯ 2 1¯ 1]).
were observed. Further examination showed that these traces distributed parallel to some slip planes, which intersected with stacking faults planes during cyclic deformation. Many speckles were thus formed, as indicated by circles in Fig. 10. It is worthy of noting that the interaction between slip bands and stacking faults separated by a ribbon was also observed, as shown in Fig. 11. Two
Fig. 11. SFs with well-defined fringes and embedded ribbon in the coarse-grain sample of 100 m fatigued at 77 K (˜g = 0 1¯ 1 3; incident beam [1¯ 2 1¯ 1]).
parallel slip bands were observed to intersect with these edge-on stacking faults resulting in the formation of speckles, as indicated by circles in Fig. 11. The similar line-up speckles were also observed in the deformed magnesium [18]. The additional dark contrasts could be attributed that pyramidal dislocations were trapped when they intercepted with the basal stacking fault plane. In other words, the speckle contrasts could come from dislocations that are bounded at the intersections of the pyramidal and basal planes. Fig. 12 is a set of TEM micrographs observed in the coarse-grained sample of 100 m. A high density of stacking faults appeared in the interior of twins, as shown in Fig. 12. For the [1¯ 2 1¯ 6] zone axis, the stacking faults were viewed edge-on and displayed a straight-line morphology. Further work is needed to confirm this structure. 4. Discussion TEM observation demonstrates that the deformed structure depends on grain size in Ti–2Al–2.5Zr alloy fatigued at 77 K. In the fine-grained sample of 5 m, twinning is a dominant deformation mode. In comparison, stacking faults with well-defined fringes become a primary plastic deformation mode in the coarse-grained samples of 40 m and 100 m. Some stacking faults separated by ribbon were produced in the region without twins. This transition of deformation mode and the corresponding microstructure could be explained in terms of growing of local stress concentration with increasing of grain size. It is well known that deformation twinning is favored as a consequence of the suppression of thermal activation of dislocations at low temperature in metals and alloys [20]. The critical resolved shear stress (CRSS) required to activate a slip system sharply increases with decreasing temperature. In comparison, the CRSS for twinning remains an approximate constant. The stress of slip would greatly surpass that of twinning, resulting in a transition of deformation mode from slip to twinning. Ambard [21] reported that only two independent slip systems, i.e., basal and prismatic slips, were activated in a titanium alloy at 20 K. Therefore, deformation twinning became the dominant plastic deformation mode in Ti–2Al–2.5Zr fatigued at 77 K. Pole mechanism is a well-known twinning mechanism for metals. According to the pole mechanism of twin nucleation proposed by Venables [22], only long jogs (>5 nm) in a secondary slip
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dislocation are a source of twining on the primary slip plane in the work-hardened fcc metals. The jogging of dislocations in the two conjugate slip systems for cold-worked materials produces these types of long jogs. The dislocation in plane where long jogs lie dissociates into a Shockley and a Frank partial according to AC = A˛ + ˛C
(1)
where AC represents a Burgers vector of dislocation. Under the action of a shear stress, the glissile Shockley partial ˛C moves away from the sessile Frank partial A˛ on the jogging plane, leaving an intrinsic fault. With the continuous operation of the twin source, the twin grows to be a biconvex lenticular shape [8]. To activate such twin source, the shear stress should be high enough along the [1 1 2] direction and there must be some stress concentration on the primary slip plane. So some stress concentration should be produced on the primary slip plane. Basal and prismatic slips with Burgers vector b = 1/31 1 2¯ 0 are the most important for hcp metals. Bacon and Martin [23] have suggested that the perfect dislocation on the basal plane would dissociate into two Shockley partial dislocations as follows: 1 1 1 1 1 2¯ 0 → 1 0 1¯ 0 + 0 1 1¯ 0 3 3 3
(2)
And then leave a stacking fault between these two partials, which are known as an extended dislocation. The relative ease of prismatic slip in hcp metal suggests that some spreading of the core could occur on the prismatic plane, and two possible dissociation forms are: 1 1 1 ¯ 1 1 2¯ 0 → 4 2 6¯ 3 + 2 4 6¯ 3 3 18 18
(3)
1 2 1 1 1 2¯ 0 → 1 1 2¯ 0 + 1 1 2¯ 0 3 9 9
(4)
Song [1] suggested that existing dislocations may be involved in a twinning process at low stresses, but they are not required for twinning at high stresses. At low stress levels, the nucleation rate of twins is sluggish because of the high nucleation energy needed. The prior slip may assist the nucleation of twin by generating a sufficient number of dislocations to offset the twinning shear at the tips of twin. In most twins, dislocations produced by primary slip appear to be insufficient for twin nucleation, given that dislocations of different Burgers vectors are needed. In this case, activation of multiple slip systems is essential for nucleation as well as for growth of twins at RT and low strain rate. Dislocation generation is more active in regions on grain boundaries than in the interior of grain, and it is more active in large grains than in small grains during deformation. Consequently, multiple slip is always initiated around grain boundaries due to a low initiation stress of dislocation slip at an approximately G/100[24]. As the testing temperature decreases to 77 K, dislocation slip is significantly restricted. In this case, activation of twin source mainly depends on shear stress during cyclic deformation. Localized stress concentration is proportional to the grain size at a given applied stress [25]. Therefore, it is much higher in coarse-grained samples than that in fine-grain samples. In the coarse grains, localized stress concentration could easily produce and offset the twinning shear in the vicinity of grain boundaries during cyclic deformation. As a result, deformation twins nucleate preferentially in region close to grain boundaries. In comparison, twin source is difficult to be activated, and then only perfect dislocation dissociate, leaving a stacking fault in the interior of grain due to insufficient local stress concentration. In the fine grains, localized stress concentration is much smaller and can be neglected. Accordingly, deformation twins form in overall gain.
Fig. 13. A comparison of dependence of twinning stress on SFE and size effect.
Grain size has a constraint effect on dislocation nucleation and slip process [26]. The stress required to activate a twinning dislocation can be written as [27] DS =
Gbp Dm
(5)
where bp is the magnitude of Burgers vector for partial dislocation, G is the shear modulus, D is the grain size and m is the shear factor. Combining the influence of grain size with crystallographic orientation and SFE, twinning stress can be expressed as [27] T = DS + SF
Gbp 1 = = + m Dm mbp
Gbp + D bp
(6)
Obviously, twinning stress is determined by the combined effect of the grain size (D), crystallographic orientation, and SFE (). As for polycrystalline titanium alloy, the influence of crystallographic orientation can be neglected. Whether grain size or SFE exerts a crucial role mainly depends on length scale. When grain size is larger than the critical grain size, size effect is relatively small and can be neglected, in comparison with SFE. In this case, twinning stress can be simplified as T =
mbp
(7)
Based on Eqs. (6) and (7), the dependence of twinning stress on SFE and grain size can be described in Fig. 13, respectively. It can be seen that the contribution of size effect to twinning stress sharply reduces as grain size increases. However, it remains nearly a constant for SFE. Therefore, the former would be inappreciable, compared with the latter to twinning stress, as grain size increases. The Burgers vector of a slip dislocation in hcp metal is the b = 1/31 1 2¯ 0 [23]. The core of this dislocation could split into two Shockley partial dislocations with a Burgers vector of b = 1/31 0 1¯ 0 connected by a stacking fault. An equilibrium separation between these two partials can be determined by a balance between the repulsive forces of the two Shockley partials and the attractive force of the SFE [28–30]. Therefore, the equilibrium split distance can be approximately expressed as d=
Gb2p 8
(8)
When an appropriate external shear stress is applied, the split distance between the Shockley partials may increase, given by the following equation d=
b2p G 8 − bp
(9)
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improvement in the LCF life of this alloy could be attributed to activation of deformation twinning, which favors compatible plastic deformation and increases the ductility of this alloy. As for Ti–2Al–2.5Zr alloy fatigued at 77 K, deformation structure evolves from twins to stacking faults as grain size increases. In other words, twin source is difficult to be activated and the typical deformation structure becomes stacking faults in coarse-grained samples. Therefore, LCF life decreases as grain size increases for Ti–2Al–2.5Zr alloy fatigued at 77 K. 5. Conclusions
Fig. 14. Relationship between applied stress and the split distance of an extended dislocation for Ti, Al and Cu.
(1) The ductility of Ti–2Al–2.5Zr alloy obviously increases, while LCF life slightly decreases as grain size increases from fine grain of 5 m to coarse grains of 40 and 100 m at 77 K. (2) Twinning is a dominant plastic deformation mode in the finegrained sample of 5 m fatigued at 77 K. As grain size increases to 40 and 100 m, streaking planar defects inside deformation twins occur. Meanwhile, stacking faults separated by ribbon appear in the region without twins. The formation of stacking faults indicates that extended dislocations are produced and become a primary plastic deformation mode during cycling. (3) Typical deformation structure evolves from deformed twins to stacking faults in Ti–2Al–2.5Zr alloy fatigued at 77 K as grain size increases. This transition of deformation mode could be attributed to the growing of localized stress concentration with increasing of grain size. Acknowledgements The authors would like to thank the National Basic Research Program of China under Grant No. 2007CB613804 and 2010CB631003 for their financial support. The financial support from the National Natural Science Foundation of China under Grant No. 50831004 and 50671077 is also greatly appreciated. References
Fig. 15. Schematic drawing of relationship between deformation structure and grain size in titanium alloy.
where is the applied shear stress. Therefore, the split distance is a function of the applied stress and the value of SFE. Because SFE is the intrinsic factor of the materials, the split distance between the Shockley partials depends on the applied stress. Fig. 14 displays the dependence of split distance on applied shear stress in titanium alloy. It can be seen that split distance will approach infinity when applied shear stress reach a critical value. In other words, the propagation of stacking faults is catastrophic under condition of a certain applied stress. The dependence of deformation structure on grain size in titanium alloy at 77 K could be schematically illustrated in Fig. 15. As for fine grain of 5 m, the typical deformation structure was observed to be deformation twins. With grain size growing to 40 and 100 m, stacking faults with well-defined fringes occurred inside twins, while stacking faults separated by ribbon also appeared in the region without twins. This result implies that forming a wide stacking fault is a prerequisite step of nucleation for a twin. Therefore, stacking faults would form more easily as grain size increases. Previous investigation results [17] indicate that a transition of plastic deformation mode occurs in Ti–2Al–2.5Zr alloy with different grain sizes and temperatures. Consequently, titanium alloy exhibited much higher ductility and longer LCF life at 77 K than those at room temperature (RT). The author suggested that the
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Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Effect of grain size on twinning behavior in Ti–2Al–2.5Zr alloy fatigued at 77 K H. Wang a,b , Q.Y. Sun a,∗ , L. Xiao a , J. Sun a a b
State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China Tubular Goods Research Institute of China National Petroleum Corporation, Xi’an 710065, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 29 July 2011 Received in revised form 9 January 2012 Accepted 24 January 2012 Available online 17 February 2012 Keywords: Low-cycle fatigue Deformation structure Twins Stacking faults Ti–2Al–2.5Zr
a b s t r a c t The low-cycle fatigue (LCF) behavior and plastic deformation mechanism were studied in Ti–2Al–2.5Zr alloy with different grain sizes of 5, 40, and 100 m fatigued at 77 K. The results show that LCF life decreases as grain size increases. Microstructural observation with transmission electron microscopy (TEM) reveals that the deformation structure evolves from twins to stacking faults as grain size increases. Deformation twinning is prevalent in the 5 m fine-grained sample. However, stacking faults with welldefined fringes were observed to occur inside deformation twins, which were separated by ribbon in coarse-grained samples of 40 and 100 m. This type of stacking faults has an implication for activating of extended dislocations during cyclic deformation. The plastic deformation mode transition could be attributed to the growing of localized stress concentration with increasing of grain size. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Twin plays a significant role in maintaining homogeneous plastic deformation in hexagonal close-packed (hcp) metals owing to their limited number of slip systems [1,2]. Up to date, twinning systems {1 1 2¯ 2}1¯ 1¯ 2 3, {1 1 2¯ 4}2¯ 2¯ 4 3 and {1 0 1¯ 1}1¯ 0 1 2 have been reported in Ti alloys [3–6]. The other possible twinning systems include {1 0 1¯ 2}, {1 1 2¯ 1} and {1 1 2¯ 3} [7]. A variety of nucleation models of twinning have been proposed depending on stacking fault energy (SFE) of materials. These models can be mainly categorized into three groups: (I) pole mechanism, which produces perfect twins without SF [8,9]; (II) models based on deviation processes, which produce intrinsic stacking fault together with the nucleation of Frank [10] or stair-rod [11–13] sessile dislocations; (III) models based on the interactions between extrinsic stacking faults [13–15]. It is well established that a slip on {1 0 1¯ 0} prism plane is the most active deformation mode in Ti. The other possible slip systems include {1 0 1¯ 1} and {1 0 2¯ 2} pyramidal slips and (0 0 0 2) basal slip. A total of only four independent deformation modes are possible by prism, basal and pyramidal slips with a Burgers vector. When a slip system with a c+ a Burgers vector is operative, this alone provides five independent deformation modes. Therefore, c+ a pyramidal slip and twinning play an important role in Ti alloys subjected to a large amount plastic deformation. Using molecular dynamic simulations (MDS), Li et al. [16] studied pyramidal slip
∗ Corresponding author. Tel.: +86 29 82668614; fax: +86 29 82663453. E-mail address: [email protected] (Q.Y. Sun). 0921-5093/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2012.01.106
in single crystal Mg, and reported that pyramidal slip was actually mediated on the {1 0 1¯ 1} plane by two independent dislocations. When these two dislocation slips combined on the surface, c+ a displacement was created. In the absence of the other dislocations, the first incomplete dislocation can leave behind a wide stacking fault on the {1 0 1¯ 1} twinning plane. We [17] investigated the effect of grain size on deformation mode in hcp titanium alloy and found a transition of plastic deformation mode from twinning together with slip to slip alone as the grain size decreased from 40 to 5 m at room temperature (RT). Deformation twins were significantly restricted at RT as grain size decreased from tens of micrometers to several microns. However, when those fine-grained samples were fatigued at 77 K, twinning was observed to be activated and became one of dominant plastic deformation modes. Consequently, the higher ductility and the longer LCF life were exhibited at 77 K than those at RT. The hcp metals have a complicated plastic deformation mode including dislocation slip with different Burgers vectors and twinning with different deformation directions and systems [13]. It is generally believed that stacking faults appear on the basal plane, and non-basal stacking faults can not form in hcp crystals because of their high SFE [16]. The stacking faults in hcp metals attract much less attention than those in fcc and bcc metals. Li et al. [18] have investigated the stacking faults and their interaction with pyramidal dislocations in plastically deformed polycrystalline pure Mg, and reported that the stacking faults consisted of well-defined fringes and streaking. The basal stacking faults were observed to be decorated by a large number of dark speckles, which were proposed to be created due to the interaction between pyramidal slip dislocations with both c and a components, themselves. The objective
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Fig. 1. Metallograph of Ti–2Al–2.5Zr samples with different grain sizes: (a) 5 m; (b) 40 m and (c) 100 m.
of this work is to study the effect of grain size on LCF behavior and to ascertain the relationship between planar slip of extended dislocations and twinning in hcp titanium alloy at low temperature, when twin plays a dominant role. 2. Experimental The material used in the present work is a commercial grade Ti–2Al–2.5Zr, which is a typical single-phase alpha titanium alloy. The initial condition of material was an extruded bar of 35 mm in diameter. These bars were further extruded to 14 mm in diameter in a hydraulic test frame so as to refine the grain size. The rods with 5 m of fine grains were produced at an extrusion temperature of about 830 ◦ C. Meanwhile, some of extruded rods were further annealed at 800 ◦ C for 2 h and 16 h in order to promote the grain growth, respectively. The diameter of coarse grains was measured to be 40 and 100 m, according to an evaluation of linear intercept method. Both fine and coarse grains were equiaxed structures, as shown in Fig. 1(a)–(c). These rods were then machined into tension and fatigue samples with 13 mm in gauge length and 7.5 mm in diameter. Both tension and symmetrical push-pull fatigue tests were performed on an INSTRON 1141 fatigue testing system. The strain rate was 6.67 × 10−4 s−1 for tension test. Symmetrical push-pull fatigue tests were performed under total displacement control in liquid nitrogen environment at 77 K. A triangular loading waveform was used with a frequency of 0.25 Hz. Double fatigue specimens were tested each strain amplitude. The stress–strain hysteresis loops were used to determine the cyclic peak stress responses and plastic strain amplitudes as a function of the number of cycles.
Specimens were soaked into a liquid nitrogen bath during testing. Tests did not carry out until the sample had been stabilized at a designed temperature of 77 K for 1 h. The detailed information about LCF experiment at 77 K had been described elsewhere [17]. After failure, deformed specimens were spark-cut within gauge. Thin foils for transmission electron microscopy (TEM) were prepared from 3-mm discs cut along cross section within gauge and thinned with a twin-jet. The fatigue dislocation substructures were observed using a JEM-200CX transmission electron microscope operated at 200 kV. 3. Results 3.1. Tensile and cyclic deformation behavior Tensile stress–strain curves of Ti–2Al–2.5Zr alloy samples with different grain sizes at 77 K are shown in Fig. 2(a). The results show that the 5 m fine-grained sample has an obvious higher strength but lower ductility than those of the 40 and 100 m coarse-grained samples. On a close examination, the coarse-grained of 100 m sample has a higher ultimate tensile strength (UTS) than that of 40 m sample due to its high strain hardening rate, even though it has lower yield stress. Yield stress decreases, while the ductility increases, as grain size increases from 40 to 100 m. Fig. 2(b) shows the effect of grain size on yield stress and elongation of Ti–2Al–2.5Zr alloy. It is demonstrated that grain size has an obvious effect on both strength and ductility. The yield stress decreases but the elongation ductility enhances as the grain size increases from 5 to 100 m. The detailed mechanical property data were summarized in Table 1. The relation between fatigue life and cyclic total strain amplitude in Ti–2Al–2.5Zr is plotted in Fig. 3. It is revealed that the
Table 1 Tensile properties of Ti–2Al–2.5Zr alloy with different grain sizes at 77 K. Grain size (m)
Yield stress (MPa)
Ultimate tensile strength (MPa)
Elongation (%)
Reduction in area (%)
Elastic module (GPa)
100 40 5
714 760 961
964 913 1116
55.0 48.8 24.3
36.2 65.5 53.3
136.6 138.2 143.6
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Fig. 2. Tensile property curves of Ti–2Al–2.5Zr with different grain sizes at 77 K. (a) Stress–strain curves and (b) yield stress/elongation vs. grain size curves.
curve of fine-grained samples of 5 m lies over that of coarsegrained samples of 40 m. Furthermore, the lifetimes of 40 m of samples are longer than those of 100 m of samples at the same strain amplitude. There is a similar linear rate of fatigue life curves between 5 m and 40 m grain samples. In comparison, the lower the cyclic total strain amplitude, the longer the LCF life is in samples with 40 m in comparison with 100 m samples. These results indicate that the fine-grained samples exhibit the longer LCF lives than those of coarse-grained samples, specifically at low cyclic strain amplitudes. 3.2. Deformation substructure 3.2.1. Twinning in fine-grained sample Deformation structures were examined in Ti–2Al–2.5Zr alloy with different grain sizes fatigued at 77 K. Fig. 4 shows a micrograph observed in sample with a grain size of 5 m fatigued at εt /2 = 2.0%. Twinning is a prevalent deformation mode. It was determined to be {1 0 1¯ 1}-type twin in the form of parallel-sides extending overall grain. Further examination showed that a streaking planar defect was produced along twin boundaries, as indicated by arrows in Fig. 4. 3.2.2. Twins and stacking faults in the coarse-grained sample of 40 m Fig. 5 shows a typical microstructure formed in the coarsegrained sample of 40 m fatigued at εt /2 = 2.0%. Deformed twins in the form of parallel-sides were also observed. Some high density of dislocations perpendicular to twin boundaries was formed
Fig. 3. Effect of grain size on the LCF life of Ti–2Al–2.5Zr at 77 K.
Fig. 4. Deformation twins formed in the fine-grained sample fatigued at 77 K (˜g = 1 0 1¯ 0; incident beam [1¯ 2 1¯ 1]).
inside these twins. The other dislocation lines aligned along twin boundaries were produced, as indicated by arrows in Fig. 5. The dislocation density inside twin is much higher than that outside one. This implies that twin boundaries (TBs) could block the moving of dislocations. When εt /2 = 4.5%, the streaking planar defects appeared inside deformation twins with parallel-sides, as shown in Fig. 6(a). On the basis of the contrast analysis with the weakbeam dark-field (WBDF) technique, the streaking planar defects accompanying with tangled dislocation occurred. Further analysis showed that these separated segments could be formed due to
Fig. 5. Deformed twins formed in the coarse-grained sample fatigued at 77 K (˜g = 1 0 1¯ 0; incident beam [1¯ 2 1¯ 1]).
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Fig. 6. Deformed twins formed in the coarse-grained samples (40 m) fatigued at 77 K: (a) bright-field image and (b) its corresponding dark-field image (˜g = 0 1¯ 1 3; incident beam [1¯ 2 1¯ 1]).
Fig. 7. Stacking faults formed inside deformed twins in coarse-grained sample fatigued at 77 K: (a) bright-field image and (b) its corresponding dark-field image, (˜g = 1 0 1¯ 0; incident beam [1¯ 2 1¯ 6]).
the intersecting among tangled dislocations, as shown in Fig. 6(b). Fig. 7 shows a set of bright-field and the weak-beam dark-field images of microstructural features inside twins. It is worth noting that several narrow fringes with dark/bright features together with streaking-like features occur inside twins, as indicated by arrows in Fig. 7(a). Some planar stacking faults were produced in the form of stair-like fringes, even though their contrast was weak, as indicated by arrows in Fig. 7(b). The similar stacking faults including long and short plates of precipitates and ribbons of stacking were observed in the solution-treated hcp Mg–Y–Zn alloys [19]. Stacking faults separated by a ribbon were observed both inside and outside twinning regions in the coarse-grained sample fatigued at εt /2 = 5.5%, as shown in Fig. 8(a). The ribbon became invisible but these stacking faults with alternative fringes were still distinct through titling the foil, as shown in Fig. 8(b). On a close examination, several mobile dislocation lines were observed to be emanated from these
stacking faults. This suggested that stacking faults could emit dislocation during cyclic deformation. Fig. 9 is a micrograph showing stacking faults formed inside and outside twinning regions, simultaneously. Stacking faults with a streak-like feature were observed inside a twin on the right of this micrograph, while stacking faults were separated by ribbon in the middle of this micrograph. In addition, the initiation of planar defects with dark/bright features was observed on the left of this micrograph. Some high density of dislocations accumulated around these initial stacking faults, indicating the nucleation of stacking faults related to the dislocation activity. 3.2.3. Stacking faults in the coarse-grained sample of 100 m Fig. 10 is a micrograph observed in the coarse-grained sample of 100 m fatigued at εt /2 = 2.5%. A large number of stacking faults with well-defined fringes emanated from the twin boundary, as indicated by arrows in Fig. 10. A few of straight deformation traces
Fig. 8. Stacking faults with fringes and an embedded ribbon in the coarse-grain sample fatigued at 77 K: (a) bright-field image and (b) dark-field image, (˜g = 0 1¯ 1 3; incident beam [1¯ 2 1¯ 1]).
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Fig. 9. Bright-field image showing stacking faults with features of streaks, stacking faults separated by ribbon and stacking faults inside twins in the coarse-grain sample fatigued at 77 K (˜g = 0 1¯ 1 3; incident beam [1¯ 2 1¯ 1]).
Fig. 12. Stacking faults inside twins in the sample with a grain size of 100 m fatigued at εt /2 = 4.5% (˜g = 1 0 1¯ 0; incident beam [1¯ 2 1¯ 6]).
Fig. 10. SFs with fringes formed in deformed twins in the coarse-grained samples of 100 m fatigued at 77 K (˜g = 0 1¯ 1 3; incident beam [1¯ 2 1¯ 1]).
were observed. Further examination showed that these traces distributed parallel to some slip planes, which intersected with stacking faults planes during cyclic deformation. Many speckles were thus formed, as indicated by circles in Fig. 10. It is worthy of noting that the interaction between slip bands and stacking faults separated by a ribbon was also observed, as shown in Fig. 11. Two
Fig. 11. SFs with well-defined fringes and embedded ribbon in the coarse-grain sample of 100 m fatigued at 77 K (˜g = 0 1¯ 1 3; incident beam [1¯ 2 1¯ 1]).
parallel slip bands were observed to intersect with these edge-on stacking faults resulting in the formation of speckles, as indicated by circles in Fig. 11. The similar line-up speckles were also observed in the deformed magnesium [18]. The additional dark contrasts could be attributed that pyramidal dislocations were trapped when they intercepted with the basal stacking fault plane. In other words, the speckle contrasts could come from dislocations that are bounded at the intersections of the pyramidal and basal planes. Fig. 12 is a set of TEM micrographs observed in the coarse-grained sample of 100 m. A high density of stacking faults appeared in the interior of twins, as shown in Fig. 12. For the [1¯ 2 1¯ 6] zone axis, the stacking faults were viewed edge-on and displayed a straight-line morphology. Further work is needed to confirm this structure. 4. Discussion TEM observation demonstrates that the deformed structure depends on grain size in Ti–2Al–2.5Zr alloy fatigued at 77 K. In the fine-grained sample of 5 m, twinning is a dominant deformation mode. In comparison, stacking faults with well-defined fringes become a primary plastic deformation mode in the coarse-grained samples of 40 m and 100 m. Some stacking faults separated by ribbon were produced in the region without twins. This transition of deformation mode and the corresponding microstructure could be explained in terms of growing of local stress concentration with increasing of grain size. It is well known that deformation twinning is favored as a consequence of the suppression of thermal activation of dislocations at low temperature in metals and alloys [20]. The critical resolved shear stress (CRSS) required to activate a slip system sharply increases with decreasing temperature. In comparison, the CRSS for twinning remains an approximate constant. The stress of slip would greatly surpass that of twinning, resulting in a transition of deformation mode from slip to twinning. Ambard [21] reported that only two independent slip systems, i.e., basal and prismatic slips, were activated in a titanium alloy at 20 K. Therefore, deformation twinning became the dominant plastic deformation mode in Ti–2Al–2.5Zr fatigued at 77 K. Pole mechanism is a well-known twinning mechanism for metals. According to the pole mechanism of twin nucleation proposed by Venables [22], only long jogs (>5 nm) in a secondary slip
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dislocation are a source of twining on the primary slip plane in the work-hardened fcc metals. The jogging of dislocations in the two conjugate slip systems for cold-worked materials produces these types of long jogs. The dislocation in plane where long jogs lie dissociates into a Shockley and a Frank partial according to AC = A˛ + ˛C
(1)
where AC represents a Burgers vector of dislocation. Under the action of a shear stress, the glissile Shockley partial ˛C moves away from the sessile Frank partial A˛ on the jogging plane, leaving an intrinsic fault. With the continuous operation of the twin source, the twin grows to be a biconvex lenticular shape [8]. To activate such twin source, the shear stress should be high enough along the [1 1 2] direction and there must be some stress concentration on the primary slip plane. So some stress concentration should be produced on the primary slip plane. Basal and prismatic slips with Burgers vector b = 1/31 1 2¯ 0 are the most important for hcp metals. Bacon and Martin [23] have suggested that the perfect dislocation on the basal plane would dissociate into two Shockley partial dislocations as follows: 1 1 1 1 1 2¯ 0 → 1 0 1¯ 0 + 0 1 1¯ 0 3 3 3
(2)
And then leave a stacking fault between these two partials, which are known as an extended dislocation. The relative ease of prismatic slip in hcp metal suggests that some spreading of the core could occur on the prismatic plane, and two possible dissociation forms are: 1 1 1 ¯ 1 1 2¯ 0 → 4 2 6¯ 3 + 2 4 6¯ 3 3 18 18
(3)
1 2 1 1 1 2¯ 0 → 1 1 2¯ 0 + 1 1 2¯ 0 3 9 9
(4)
Song [1] suggested that existing dislocations may be involved in a twinning process at low stresses, but they are not required for twinning at high stresses. At low stress levels, the nucleation rate of twins is sluggish because of the high nucleation energy needed. The prior slip may assist the nucleation of twin by generating a sufficient number of dislocations to offset the twinning shear at the tips of twin. In most twins, dislocations produced by primary slip appear to be insufficient for twin nucleation, given that dislocations of different Burgers vectors are needed. In this case, activation of multiple slip systems is essential for nucleation as well as for growth of twins at RT and low strain rate. Dislocation generation is more active in regions on grain boundaries than in the interior of grain, and it is more active in large grains than in small grains during deformation. Consequently, multiple slip is always initiated around grain boundaries due to a low initiation stress of dislocation slip at an approximately G/100[24]. As the testing temperature decreases to 77 K, dislocation slip is significantly restricted. In this case, activation of twin source mainly depends on shear stress during cyclic deformation. Localized stress concentration is proportional to the grain size at a given applied stress [25]. Therefore, it is much higher in coarse-grained samples than that in fine-grain samples. In the coarse grains, localized stress concentration could easily produce and offset the twinning shear in the vicinity of grain boundaries during cyclic deformation. As a result, deformation twins nucleate preferentially in region close to grain boundaries. In comparison, twin source is difficult to be activated, and then only perfect dislocation dissociate, leaving a stacking fault in the interior of grain due to insufficient local stress concentration. In the fine grains, localized stress concentration is much smaller and can be neglected. Accordingly, deformation twins form in overall gain.
Fig. 13. A comparison of dependence of twinning stress on SFE and size effect.
Grain size has a constraint effect on dislocation nucleation and slip process [26]. The stress required to activate a twinning dislocation can be written as [27] DS =
Gbp Dm
(5)
where bp is the magnitude of Burgers vector for partial dislocation, G is the shear modulus, D is the grain size and m is the shear factor. Combining the influence of grain size with crystallographic orientation and SFE, twinning stress can be expressed as [27] T = DS + SF
Gbp 1 = = + m Dm mbp
Gbp + D bp
(6)
Obviously, twinning stress is determined by the combined effect of the grain size (D), crystallographic orientation, and SFE (). As for polycrystalline titanium alloy, the influence of crystallographic orientation can be neglected. Whether grain size or SFE exerts a crucial role mainly depends on length scale. When grain size is larger than the critical grain size, size effect is relatively small and can be neglected, in comparison with SFE. In this case, twinning stress can be simplified as T =
mbp
(7)
Based on Eqs. (6) and (7), the dependence of twinning stress on SFE and grain size can be described in Fig. 13, respectively. It can be seen that the contribution of size effect to twinning stress sharply reduces as grain size increases. However, it remains nearly a constant for SFE. Therefore, the former would be inappreciable, compared with the latter to twinning stress, as grain size increases. The Burgers vector of a slip dislocation in hcp metal is the b = 1/31 1 2¯ 0 [23]. The core of this dislocation could split into two Shockley partial dislocations with a Burgers vector of b = 1/31 0 1¯ 0 connected by a stacking fault. An equilibrium separation between these two partials can be determined by a balance between the repulsive forces of the two Shockley partials and the attractive force of the SFE [28–30]. Therefore, the equilibrium split distance can be approximately expressed as d=
Gb2p 8
(8)
When an appropriate external shear stress is applied, the split distance between the Shockley partials may increase, given by the following equation d=
b2p G 8 − bp
(9)
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improvement in the LCF life of this alloy could be attributed to activation of deformation twinning, which favors compatible plastic deformation and increases the ductility of this alloy. As for Ti–2Al–2.5Zr alloy fatigued at 77 K, deformation structure evolves from twins to stacking faults as grain size increases. In other words, twin source is difficult to be activated and the typical deformation structure becomes stacking faults in coarse-grained samples. Therefore, LCF life decreases as grain size increases for Ti–2Al–2.5Zr alloy fatigued at 77 K. 5. Conclusions
Fig. 14. Relationship between applied stress and the split distance of an extended dislocation for Ti, Al and Cu.
(1) The ductility of Ti–2Al–2.5Zr alloy obviously increases, while LCF life slightly decreases as grain size increases from fine grain of 5 m to coarse grains of 40 and 100 m at 77 K. (2) Twinning is a dominant plastic deformation mode in the finegrained sample of 5 m fatigued at 77 K. As grain size increases to 40 and 100 m, streaking planar defects inside deformation twins occur. Meanwhile, stacking faults separated by ribbon appear in the region without twins. The formation of stacking faults indicates that extended dislocations are produced and become a primary plastic deformation mode during cycling. (3) Typical deformation structure evolves from deformed twins to stacking faults in Ti–2Al–2.5Zr alloy fatigued at 77 K as grain size increases. This transition of deformation mode could be attributed to the growing of localized stress concentration with increasing of grain size. Acknowledgements The authors would like to thank the National Basic Research Program of China under Grant No. 2007CB613804 and 2010CB631003 for their financial support. The financial support from the National Natural Science Foundation of China under Grant No. 50831004 and 50671077 is also greatly appreciated. References
Fig. 15. Schematic drawing of relationship between deformation structure and grain size in titanium alloy.
where is the applied shear stress. Therefore, the split distance is a function of the applied stress and the value of SFE. Because SFE is the intrinsic factor of the materials, the split distance between the Shockley partials depends on the applied stress. Fig. 14 displays the dependence of split distance on applied shear stress in titanium alloy. It can be seen that split distance will approach infinity when applied shear stress reach a critical value. In other words, the propagation of stacking faults is catastrophic under condition of a certain applied stress. The dependence of deformation structure on grain size in titanium alloy at 77 K could be schematically illustrated in Fig. 15. As for fine grain of 5 m, the typical deformation structure was observed to be deformation twins. With grain size growing to 40 and 100 m, stacking faults with well-defined fringes occurred inside twins, while stacking faults separated by ribbon also appeared in the region without twins. This result implies that forming a wide stacking fault is a prerequisite step of nucleation for a twin. Therefore, stacking faults would form more easily as grain size increases. Previous investigation results [17] indicate that a transition of plastic deformation mode occurs in Ti–2Al–2.5Zr alloy with different grain sizes and temperatures. Consequently, titanium alloy exhibited much higher ductility and longer LCF life at 77 K than those at room temperature (RT). The author suggested that the
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