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Grain size effect on deformation mechanisms and mechanical properties of titanium
Journal Pre-proof Grain size effect on deformation mechanisms and mechanical properties of titanium Z.W. Huang, P.L. Yong, H. Zhou, Y.S. Li PII:
S0921-5093(19)31507-2
DOI:
https://doi.org/10.1016/j.msea.2019.138721
Reference:
MSA 138721
To appear in:
Materials Science & Engineering A
Received Date: 6 July 2019 Revised Date:
19 November 2019
Accepted Date: 21 November 2019
Please cite this article as: Z.W. Huang, P.L. Yong, H. Zhou, Y.S. Li, Grain size effect on deformation mechanisms and mechanical properties of titanium, Materials Science & Engineering A (2019), doi: https://doi.org/10.1016/j.msea.2019.138721. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
Grain size effect on deformation mechanisms and mechanical properties of titanium Z. W. Huang, P. L. Yong, H. Zhou, Y. S. Li* Nano and Heterogeneous Structural Materials Center, School of Materials Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
Corresponding author: Professor Yusheng Li, First author: Zhaowen Huang. Corresponding authors e-mail addresses: [email protected] (Yusheng Li).
Abstract The grain size effect on deformation mechanisms and mechanical properties of Ti is investigated by using electron backscattered diffraction technique. Higher twin density and more twin systems are found in Ti with larger grain size after cryogenic rolling process. The percentage of twinned grain increases rapidly first and then become steady until saturation, while the number of twin per grain keeps increasing with the increase of grain size. The generation of {1122} contraction twin is shown a higher sensitivity to grain size than that of {1012} extension twin. Annealed Ti with smaller grain size possesses better work hardening. While after rolling process, Ti with lager grain size obtains better work hardening due to higher twin density and lower density of pre-existing dislocations.
Key words: Titanium; twinning; slip; grain size; mechanical property.
Grain size effect on deformation mechanisms and mechanical properties of titanium Z. W. Huang, P. L. Yong, H. Zhou, Y. S. Li* Nano and Heterogeneous Structural Materials Center, School of Materials Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
Abstract The grain size effect on deformation mechanisms and mechanical properties of Ti is investigated by using electron backscattered diffraction technique. Higher twin density and more twin systems are found in Ti with larger grain size after cryogenic rolling process. The percentage of twinned grain increases rapidly first and then become steady until saturation, while the number of twin per grain keeps increasing with the increase of grain size. The generation of {1122} contraction twin is shown a higher sensitivity to grain size than that of {1012} extension twin. Annealed Ti with smaller grain size possesses better work hardening. While after rolling process, Ti with lager grain size obtains better work hardening due to higher twin density and lower density of pre-existing dislocations.
Key words: Titanium; twinning; slip; grain size; mechanical property.
1. Introduction Twinning is important in HCP materials to accommodate deformation strain along the c-axis, since all of the easy slip directions are perpendicular to the c-axis [1-3]. Deformation twin would induce lattice re-orientation of the matrix, while slip is more uniform in strain accommodation. In some cases, {1122} contraction twin (CT) rotates the matrix to a “softer” orientation, leading to better work hardening, while {1012} extension twin (ET) induces a “harder” orientation [4]. Twin boundary could act as barrier to dislocation movement, and has great influence on the flow stress and work hardening behavior of materials [5, 6].
Temperature and strain rate are found to influence the twinning and slip behaviors in HCP materials, e.g., twinning is favored at low temperature and high strain rate while slip is suppressed in these conditions [7]. Besides, grain size is also reported to have influence on the twinning behavior of materials [8-11]. Twins with larger length and thickness were observed in parent grains with larger size, and the twin aspect ratios were also increased with an increase of grain size [12]. Twin volume fraction is found strongly depended on grain size in Ti, while it is almost insensitive to grain size in Mg [12]. Some other studies reported that the twinning probability is independent on the grain size, even the twinning stress decreases with increasing grain size [13, 14]. The increase number of twins per grain could be attributed to the increasing grain boundary area in larger grain [15]. To date, many researchers have investigated the twinning behavior in grains with different size scale via statistical analysis. However, little attention has been paid to the generation of high order twins, e.g., secondary twin, and the variants formation of different twin systems in parent grains with different size scale. Besides, some questions concerning the relationship between deformation mechanisms and the mechanical properties in Ti samples with different grain size remain unanswered. The aim of this research is to investigate the grain size effect on deformation mechanisms and mechanical properties of Ti. Samples were annealed at different temperature to achieve grain size variations. Further rolling treatment was performed at cryogenic temperature with the rolling reduction of 8 %. Electron backscattered diffraction (EBSD) technique was employed to observe microstructures and obtain statistical results. Quasi-static uniaxial tensile test was used to analyze the mechanical properties. 2. Experimental Materials used in this study were commercially pure titanium with chemical composition of (wt. %): Al 0.19, V 0.13, Fe 0.147, Zr 0.098, Cr 0.033, and balance Ti. The as-received Ti was annealed in nitrogen atmosphere at 550℃, 650℃ and 750℃ for 1h respectively, followed by furnace cooling, to obtain samples with different grain sizes and to diminish flaws and residual stress. Before rolling treatment, Ti
samples were polished with abrasive paper to remove oxidations and contaminants on the surface. Samples with different grain size were rolled at liquid nitrogen temperature (LNT) for one pass, with a rolling reduction of 8 %. Before EBSD observation, these annealed and rolled Ti were electro-polished in a mixture of perchloric acid and acetic with 1:9 in volume ratio. EBSD analysis was performed with a FEI Quant 250 field emission scanning electron microscope. The electron beam energy was set to 12 kV. The scanning step size was 0.25 µm and the indexing rate was kept above 85 % to ensure the data veracity. Channel 5 software was used to analysis the EBSD data, for orientation mapping, misorientation distribution analysis and boundary calculation. Uniaxial tensile tests were carried out on a tensile tester, with a strain rate of 3 × 10-3 / s at room temperature, and all of the tests were performed at least three times. 3. Results 3.1. Slip and twinning behaviors The cross-sectional EBSD morphologies of annealed and rolled Ti are shown in Fig. 1. Boundaries with misorientation between 2° to 15° are identified as low angle grain boundaries (LAGBs) and colored by sliver. Those boundaries with misorientation larger than 15° are identified as high angle grain boundaries (HAGBs) and colored by black in all the EBSD images. Grains with misorientations larger than 15° are identified as individual grains, including deformation twins. Since twins would rotate the matrix to different orientations according to definite crystallographic relationship, e.g., 65°/< 1010 > for {1122} and 85°/< 1120 > for {1012} [2], regions in the matrix with corresponding relationship are identified as twins in this work. After annealing at 550 ℃, 650 ℃ and 750 ℃, twinning-free equiaxial grains are introduced in Ti with an average grain size of 4 µm, 10 µm and 50 µm, respectively. After rolling at LNT with the reduction of 8 %, the average grain size of Ti decreases to 1.9 µm, 3.2 µm and 5.1 µm respectively. Note that the average grain size calculated in the research is area average, which is extracted from the EBSD data by using HKL software. After rolling treatment, deformation twins are stimulated to accommodate the strain. Parallel twin lamellae, secondary twin and twin-twin
intersection are detected in parent grains [16, 17]. Fig. 2 gives the texture distributions of annealed and rolled Ti, e.g., (0002) planes and < 1120 > directions. While x and y axs parallel to RD and ND shown in Fig. 1. After annealing, grains are orientated with [0002] axes rotate from ND towards RD, with the deviation angle of ~30°, which reveals typical double peaks texture in Ti [18]. Grain orientations in annealed Ti with different size scale are similar as can be seem from Fig. 2 a-c. After rolling process, density of twins generate in Ti (Fig. 1d-f). Under the effect of twinning, grains are rotated to the orientations with (0002) planes perpendicular to z axis, which parallels to TD (Fig. 2d-f). The distribution of < 1120 > directions becomes more randomly compared with annealed Ti. Misorientation distribution images of annealed and rolled Ti with different grain size are shown in Fig. 3. The bin size used to generate the figure is 1°. No obvious misorientation peak is found in annealed Ti, i.e., black histograms in Fig. 3 a-c. After rolling treatment, only one obvious misorientation peak around 65° is detected in Ti with the average grain size of 4 µm (Fig. 3a). It is corresponding to {1122} CT in HCP material, which rotates the matrix by 65° along < 1010 > [19]. With the grain size increasing, other misorientation peaks around 77° and 85° are found in Ti as shown in Fig. 3b and c, and they are corresponding to {1124} CT and {1012} ET respectively [18]. The misorientation peak of {1122} CT is obviously higher than that of {1124} CT and {1012} ET. While the intensity of {1124} CT and {1012} ET peaks is nearly equivalent. Results reveal that the number of twinning system increases with increasing grain size, and {1122} CT is the dominating twinning system in rolled Ti when deformed at cryogenic temperature [18].
Fig. 1 Cross-sectional EBSD images of annealed Ti with the grain size of (a) 4 µm, (b) 10 µm, (c) 50 µm, and rolled Ti with the grain size of (d) 4 µm, (e) 10 µm, (f) 50 µm.
Fig. 2 Texture distributions of annealed Ti with the grain size of (a) 4 µm, (b) 10 µm, (c) 50 µm, and rolled Ti with the grain size of (d) 4 µm, (e) 10 µm, (f) 50 µm.
Fig. 4 gives the boundary fraction calculation results of annealed and rolled Ti, including LAGBs, HAGBs and twin boundaries. The LAGB and HAGB percentage
in annealed Ti with different grain size is almost equivalent (Fig. 4a), with a value of 10.8 ± 0.4 % and 89.2 ± 0.4 %, respectively. After rolling process, the LAGB percentage of Ti with the average grain size of 4 µm increases rapidly to 25.0 %, with an increment of 13.8 % (Fig. 4b). It implies a severe dislocation accumulation in Ti with small grain size during rolling process [20]. While a relatively low twin boundary percentage (15.4 %) is detected in the sample. As the average grain size increases to 10 µm and 50 µm, the LAGB percentage decreases to 14.9 % and 13.7 %, and the twin boundary percentage increases to 28.3 % and 30.0 % respectively. It proves the concept that twinning is favored in Ti with larger grain size, which is consistent with previous investigations [12].
Fig. 3 Misorientation distributions of annealed Ti (black histograms) and rolled Ti (red histograms) with the average grain size of (a) 4 µm, (b) 10 µm, (c) 50 µm.
Fig. 4 (a) LAGB and HAGB percentage in annealed Ti and (b) LAGB, TB and HAGB percentage in LNT-rolled Ti with different grain size.
3.2. Twinning variations Grain size effect on the generation of primary, secondary twin and the activation of different twin systems in Ti is investigated, and the statistical results are shown in Fig. 5. Parent grains with size scale range from 1 µm to 80 µm are taken into consideration in this research. Fig. 5a gives the percentage of parent grain containing primary and secondary twin. With an increase of grain size, the percentage of twinned grain increases rapidly first, then reach a critical value and become steady until saturation. The critical grain size for primary twin is ~10 µm, which indicates that primary twins generate in over 90 % of the grains with size no less than 10 µm. Besides, the critical grain size for secondary twins is ~17 µm, and over 70 % of the grains with larger size contain secondary twins. Since the twin size strongly depends on the grain size, larger parent grain is required to generate high order twin, e.g., secondary twin. Fig. 5b gives the number of twins per grain in parent grains with different size. The number of twin increases from no more than 2 twins in parent grain with the size of 1 µm to over 16 twins in parent grain with the size of ~75 µm, and this tendency is consistent with previous investigation [12]. Similarly, the number of primary and
secondary twin increases with increasing grain size. While the number of primary twin per grain is larger than that of secondary twin in parent grain with the same size. Fig. 5c gives the number of twin variants per grain with different grain size. Four common twin systems are taken into consideration in the research, e.g., {1121} , {1012} ETs and {1122}, {1124} CTs. Results show that the number of twin variant per grain increases with an increase of grain size. The number of {1122} CT is the highest in parent grain with the same size. It reveals that {1122} CT is the dominant twinning system in Ti when deformed at cryogenic temperature [18], and this is consistent with the misorientation peak intensity shown in Fig. 3. The number of {1012} ET is the second highest, while a few {1121} ET and {1124} CT is detected. Notice that the slope of {1122} CT is higher than that of {1012} ET, which implies that the generation of {1122} CT is more sensitive to grain size. The slopes of {1121} ET and {1124} CT are the lowest in the study.
Fig. 5 Distributions of (a) percentage of parent grain containing primary twin / secondary twin
among all the detected grains, (b) number of all twin / primary twin / secondary twin per grain, and (c) number of different twin variant per grain in Ti, with the increase of grain size.
As discussed, the grain size effect on the generation of different twin variants is different. The total number fraction of {1121} ET and {1124} CT is calculated smaller than 5 % in this research, and these two variants are not taken into further discussion. For the dominant {1122} CT and {1012} ET, the slope of {1122} CT is higher, indicating a higher sensitivity to the grain size. Fig. 6 gives a typical morphology of areas containing {1122} CT and {1012} ET in rolled Ti. Results show that {1012} ETs are with prism structure and take up a large volume fraction of the parent grain. No more than two twins can be observed in a grain simultaneously. While {1122} CTs show lamellae structure, and up to 4 twins can be found in a grain. It is because the twinning shear of {1012} ET (0.175) is smaller than that of {1122} CT (0.218), and a larger volume fraction is required for {1012} ET to accommodate the same deformation strain as {1122} CT [1, 18]. The formation of {1012} ET takes up a large volume fraction of the parent grain, and the generation of subsequent variant becomes difficult due to higher twinning stress in smaller grain.
Fig. 6 EBSD images of area containing (a) {1122} CTs and (b) {1012} ETs in LNT-rolled Ti samples with the average grain size of 4 µm.
3.3. Mechanical properties Fig. 7 gives the typical tensile test curves of annealed and rolled Ti, and the corresponding statistical results are shown in table 1. Annealed and rolled Ti samples
with different grain size are coded as 1 # to 6 #. Results reveal that annealed Ti with the average grain size of 4 µm has the highest strength, e.g., yield stress ( MPa) and ultimate tensile stress ( (
� ,
381
, 450 MPa), and the largest uniform elongation
, 13.3 %). With the increase of grain size, the yield stress and uniform elongation
decrease simultaneously, which is consistent with previous investigation [21]. After rolling process, Ti with smaller grain size possess higher strength but with lower tensile ductility. Fig. 7b gives the work hardening curves and the true strain-stress curves of annealed and rolled Ti. The work hardening rate (θ) is given by θ = ∂σ/ ∂ε, where σ is the true stress and ε is the true strain of the sample. Results show that smaller grain size leads to better work hardening in annealed Ti. On the contrary, better work hardening is detected in Ti with larger grain size after rolling.
Fig. 7 (a) Tensile engineering strain-stress curves of annealed and rolled Ti samples with different grain size, and (b) corresponding true strain-stress curves and work hardening rate curves. Table 1 Mechanical property statistic of annealed and rolled Ti. Sample 1# 2# 3# 4# 5# 6# *
: yield stress;
Engineering stress/strain /MPa /MPa ! "#/% 381 310 249 525 505 483
450 405 268 605 575 556
0.133 0.127 0.113 0.021 0.041 0.050
: ultimate tensile stress;
True stress/strain /MPa 385 313 251 552 507 493
/MPa 515 460 425 610 600 585
!
"# /%
0.138 0.132 0.118 0.022 0.042 0.051
: uniform elongation.
Notice that for rolled Ti, the strain path changes from rolling (plane strain
deformation) to tension during the test, which is an orthogonal strain path change. Due to various strain states, the generation of different slip systems may have influence on the yield points of Ti samples, e.g., lower mobile dislocation density. Hence, Schmid law is used to study the slip activities of Ti samples under different strain path. Fig. 8 and Fig. 9 give the Schmid factor distributions of Ti samples during annealing and sequential rolling treatments. All the four slip systems, i.e., basal, prismatic, pyramidal and pyramidal slip are taken into consideration [22]. During rolling and tensile treatments, the loading stresses are parallel to ND and RD respectively, as shown in Fig. 1. During rolling process, Schmid factor calculation results show that the most active slip system is basal slip, with the average Schmid factor of 0.402, and over 84.7 % of the pixels are with soft orientations (with Schmid factor larger than 0.3, Fig. 8a). While prismatic slip is the hardest to be stimulated due to the lowest Schmid factor (with the value of 0.199, Fig. 8b). Because of similar texture as shown in Fig. 2, Ti samples with different grain sizes show similar Schmid factor distribution tendency.
Fig. 8 Schimid factor distributions of different slip systems in (a-d) 1# annealed Ti, (e-h) 2# annealed Ti, (i-l) 3# annealed Ti during rolling treatment, the loading stress parallels to ND. Percentage of pixels with hard orientations (0-0.3), soft orientations (0.3-0.5) and the average Schmid factors are given.
After rolling treatment, Schmid factor distributions of rolled Ti during tensile test are shown in Fig. 9. Results show that pyramidal slip with the average Schmid factor of 0.392 is the most possible to generate, while basal sip with the average Schmid factor of 0.229 is the hardest to be stimulated, which is distinctly different from Ti during rolling treatment. It is because the strain path changes significantly from plane strain to tensile strain as discussed, and which is beneficial to stimulate pyramidal slip. It is known that Schmid factor denotes the resolved shear stress (RSS) of applied stress (
$%%& '( )
on corresponding slip planes. On the contrary, if the critical resolved
shear stress (CRSS) and Schmid factors of the slip systems are known, the
$%%& '(
needed to stimulate the dislocation can be calculated by: $%%& '(
=
)*++ /,
(1)
Where m is the Schmid factor of corresponding slip system. In this study, the average Schmid factors of different slip systems are calculated by using HKL software. The CRSS requires to generate basal slip, prismatic slip and pyramidal slip are calculated as: 150 MPa, 30 MPa and 120 MPa respectively [23]. Hence, the
$%%& '(
needed to
activate slip systems in Ti during rolling and tensile treatments can be calculated, and results are shown in table 2.
Fig. 9 Schimid factor distributions of different slip systems in (a-d) 4# rolled Ti, (e-h) 5# rolled Ti, (i-l) 6# rolled Ti during tensile process, the loading stress parallels to RD. Percentage of pixels
with hard orientations (0-0.3), soft orientations (0.3-0.5) and the average Schmid factors are given.
During rolling process, the
$%%& '(
requires to generate prismatic slip is
the lowest in Ti samples, in spite of corresponding low Schmid factor. Hence, prismatic dislocation generates and accumulates during rolling treatment, resulting in the increase of LAGBs (Fig. 4). During tensile process, the texture is favorable to generate prismatic slip, and the
$%%& '(
requires to stimulate the dislocation is
obviously lower than that to generate other dislocations. That is to say, prismatic slip is the dominant slip system in Ti during rolling and tensile treatment, and the generation of dislocation becomes easier when deformed along tensile direction. Hence, strength increment of the yield points may not be attributed to the lower mobile dislocation density, and could be relative to dislocation strengthening and grain boundary strengthening.
Table 2 Applied stress (MPa) needed to generate different slip systems in Ti during rolling and tensile processes. Rolling process 1# Annealed Ti 2# Annealed Ti 3# Annealed Ti
Basal 373 374 386
Prismatic 151 210 214
Pyramidal 344 370 379
Pyramidal 378 344 348
Pyramidal 306 317 326
Pyramidal 308 302 293
Tensile process 4# Rolled Ti 5# Rolled Ti 6# Rolled Ti
Basal 655 711 761
Prismatic 78 81 83
After yielding, with the increase of flow stress, slip and twinning are triggered to accommodate the local strain and contribute to work hardening. With the tensile process continues, dislocation and twinning behaviors may induce dynamic softening in Ti. In this research, grain size variation leads to different degrees of dislocation accumulation and twin boundary fraction in Ti (Fig. 4b), thus influence the dynamic softening process during tensile test. Qin et al. [23] reported that the initiation of
twinning and dynamic softening, e.g., dynamic recrystallization (DRX), can be detected from the following condition: -
-.
/−
-1
-.
2=0
(2)
From the equation, three points of inflection in each of the curves can be derived, and they are corresponding to two minima and one maximum [24]. The first minimum point is associated with the initiation of twinning, and the second relates to the initiation of dynamic recrystallization. While the maximum point indicates a decrease in the twinning rate. Besides to twinning and DRX, dislocation activities could be another influence factor of dynamic softening, since dislocation recovery may occurs with continues dislocation accumulation. The work hardening derivative on true stress (− 4564 ) curves of annealed and rolled Ti are shown in Fig. 10. The first minimum point is not prominent in annealed Ti with the average grain size of 4 µm and 10 µm (Fig. 10a, b). While the critical stress for the second point is lower in Ti with larger grain size, e.g., 480 MPa for Ti with the average grain size of 10 µm and 530 MPa for Ti with the average grain size of 4 µm. For Ti with the average grain size of 50 µm, twinning occurs when the stress reaches 380 MPa (Fig. 10c). As the stress increases to 440 MPa, dynamic softening happens in Ti. This critical stress for dynamic softening is the lowest among all the annealed samples. After rolling treatment, the two minima points are obvious in Ti (Fig. 10d-f). With the grain size increase, the critical stress for twinning decreases from 608 MPa to 564 MPa, and from 627 MPa to 590 MPa for dynamic softening. It reveals that both twinning and dynamic softening become easier during tensile test in Ti with larger grain size.
Fig. 10 Work hardening derivative on true stress curves of (a-c) anneal Ti and (d-f) rolled Ti with different grain size. The upward and the downward black arrows represent the first and the second minima points respectively.
4. Discussion In HCP materials, the critical resolved shear stress for twinning decreases with the increase of grain size [1]. It is widely reported that twin boundary could act as barrier to dislocation movement, thus resulting in higher strength [25, 26]. In order to investigate the contribution of twin boundary to the strength increment of Ti, Hall-Petch relationship is considered in this research. According to the relationship, grain boundary strengthening of materials can be calculated by: σ= Where
8
8
+ :; <
=6 >
(3)
is the friction stress and k is a constant. Assuming that pre-existing
dislocations are recovered and annihilated after annealing treatment, the yield stress of annealed Ti primarily attributes to grain boundary strengthening. The yield stress of 1#-3# annealed Ti with average grain size of 4 µm, 10 µm and 50 µm are 381 MPa, 310 MPa and 249 MPa respectively (table 1). Hence,
8
and k are calculated 196
MPa and 0.368 MPam1/2 as shown in Fig. 11. After rolling treatment, average grain size of 4#-6# rolled Ti decreases to 1.9 µm, 3.2 µm and 5.1 µm as discussed. According to Hall-Petch relationship, the yield stress increases to 462 MPa, 402 MPa and 359 MPa, with the increment of 81 MPa, 92 MPa and 110 MPa respectively.
Higher yield stress increment of Ti with larger grain size after rolling treatment could be attributed to higher twin volume fraction as shown in Fig. 4. Besides, dislocation accumulation contributes to the additional stress increment of Ti before yielding. Generally, the Hall-Petch fitting is fine in this research, but the resistance of twin boundaries to dislocations is not the same as that of random HAGBs. However, since little data is available, only grain size including twin size is fitted using Hall-Petch relationship.
Fig. 11 Hall-Petch relationship of annealed Ti
In addition to the strength increment, higher twin density also contributes to better work hardening. Assuming that the imposed deformation strain on Ti is equivalent during rolling process. Either twinning or slip is stimulated to accommodate the strain. Twinning is active in Ti with larger grain size as discussed, and high density of twin accommodates a larger portion of the strain. Thus, relatively lower density of dislocation generates to release the strain. It results in higher twin boundary percentage and lower LAGB percentage in Ti with larger grain size (Fig. 4b). Firstly, because of low density of pre-existing dislocations, rolled Ti with larger grain size possess better work hardening during tensile test. On the contrary, twinning is hard to generate in Ti with smaller grains because of higher twinning stress. Slip is stimulated to accommodate the strain, resulting in high density of pre-existing dislocations and worse work hardening. Secondly, twinning could rotate the parent grain to the orientation in favor of slip. Therefore, rolled Ti with higher twin boundary fraction possess better work hardening.
As is known, dynamic hardening and dynamic softening exist simultaneously during tensile process. The former relates to slip and the latter derives from twinning, slip and continuous DRX [9]. For annealed Ti with small grain size (4 µm), slip is the dominating deformation mechanism during tensile test. Dislocation generates and tangles with increasing stress, areas containing high dislocation density could serve as site for continuous DRX because of high stored energy [27]. Since certain extent of dislocation accumulation is required to trigger continuous DRX and dislocation recovery, critical stress for the second minimum point is relatively higher as shown in Fig. 10a. With the grain size increase to 10 µm, twinning becomes easier in Ti. However, since the twin volume fraction is still in low level, the first minimum point for twinning is not prominent as shown in Fig. 10b. Notice that the slope of the curve changes with the increase of stress, therefore the curve can be divided into three stages: stage 1, dislocation tangle; stage 2, twinning occurs; stage 3, decrease of twinning rate. As the grain size keep increasing, higher twin volume fraction is introduced, and the first minimum point for twinning becomes obvious. Yan et al. [27] investigated that twin boundary could serve as site for DRX because of high stored energy, thus promote the occurrence of DRX. Hence, dynamic softening becomes easier in Ti with larger grain size, leads to lower stress for the second minimum point. After rolling treatment, high dislocation density generates in Ti with small grain size (4 µm), with the LAGB percentage of 25.0 % as shown in Fig. 4b. Dislocation accumulation can not only be the site for continuous DRX, but also promote twinning due to high stored energy [2]. Therefore, the first minimum point for twinning appears when the stress reaches 608 MPa (Fig. 10d). Besides, twin boundary fraction increases with increasing grain size. It leads to the lower critical stress to stimulate twinning and dynamic softening during tensile process. 5. Conclusion Ti samples with different grain size are studied to investigate the grain size effect on their deformation mechanisms and mechanical properties, and following conclusions can be drawn: (1) Twin boundary fraction and the number of active twinning system increase with
the increase of grain size in Ti during rolling treatment. While higher dislocation density is detected in Ti with smaller grain size. (2) The percentage of parent grain containing primary and secondary twin increases rapidly first and then becomes steady with the increase of grain size. The critical grain size for the percentage increment of primary and secondary twin is 10 µm and 17 µm respectively. Besides, the twin number increment of primary twin is larger than that of secondary twin with increasing grain size. (3) The twin number per grain of {1122} CT is more sensitive to grain size than that of {1012} ET, which is related to the twinning shear and twin morphology. The generation of {1012} ET would consume lager volume fraction of parent grain than that of {1122} CT, thus hinder the formation of subsequent twin. (4) Annealed Ti with smaller grain size possess higher strength, larger uniform elongation and better work hardening. A larger strength increment is calculated in Ti with larger grain size after rolling, because of higher twin boundary fraction. Besides, high twin density and low pre-existing dislocations accumulation contribute to better work hardening of rolled Ti with large grain size.
Acknowledgements This work was supported by the National Key R&D Program of China (2017YFA0204403), National Natural Science Foundation of China (51741106), Natural Science Foundation of Jiangsu Province (BK20191292), the Fundamental Research Funds for the Central Universities (30919011256), the Jiangsu Key Laboratory of Advanced Micro & Nano Materials and Technology, and Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX18_0415). EBSD was performed in the Materials Characterization and Research Center of the Nanjing University of Science and Technology.
Data availability The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.
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[22] M.H. Yoo, C.T. Wei, Slip Modes of Hexagonal‐Close‐Packed Metals, J. Appl. Phys. 38 (1967) 4317-4322. [23] H. Qin, J.J. Jonas, H. Yu, N. Brodusch, R. Gauvin, X. Zhang, Initiation and accommodation of primary twins in high-purity titanium, Acta Mater. 71 (2014) 293-305. [24] X. Liu, J. Jonas, L.X. Li, B. Zhu, Flow softening, twinning and dynamic recrystallization in AZ31 magnesium, Mater. Sci. Eng. A 583 (2013) 242-253. [25] S. Ziaei, M.A. Zikry, The effects of twins on the large strain deformation and fracture of hexagonal close packed crystalline materials, Acta Mater. 120 (2016) 435-442. [26] G.D. Liu, R.L. Xin, F.Y. Liu, Q. Liu, Twinning characteristic in tension of magnesium alloys and its effect on mechanical properties, Mater. Des. 107 (2016) 503-510. [27] C.K. Yan, A.H. Feng, S. Qu, G.J. Cao, J.L. Sun, J. Shen, D.L. Chen, Dynamic recrystallization of titanium: Effect of pre-activated twinning at cryogenic temperature, Acta Mater. 154 (2018) 311-324.
Authors' contributions: ZW Huang performed the experiment and analysis; PL Yong helped with the sample preparation; H Zhou and YS Li proposed the idea, designed the experiment and responsible for the paper.
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
S0921-5093(19)31507-2
DOI:
https://doi.org/10.1016/j.msea.2019.138721
Reference:
MSA 138721
To appear in:
Materials Science & Engineering A
Received Date: 6 July 2019 Revised Date:
19 November 2019
Accepted Date: 21 November 2019
Please cite this article as: Z.W. Huang, P.L. Yong, H. Zhou, Y.S. Li, Grain size effect on deformation mechanisms and mechanical properties of titanium, Materials Science & Engineering A (2019), doi: https://doi.org/10.1016/j.msea.2019.138721. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
Grain size effect on deformation mechanisms and mechanical properties of titanium Z. W. Huang, P. L. Yong, H. Zhou, Y. S. Li* Nano and Heterogeneous Structural Materials Center, School of Materials Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
Corresponding author: Professor Yusheng Li, First author: Zhaowen Huang. Corresponding authors e-mail addresses: [email protected] (Yusheng Li).
Abstract The grain size effect on deformation mechanisms and mechanical properties of Ti is investigated by using electron backscattered diffraction technique. Higher twin density and more twin systems are found in Ti with larger grain size after cryogenic rolling process. The percentage of twinned grain increases rapidly first and then become steady until saturation, while the number of twin per grain keeps increasing with the increase of grain size. The generation of {1122} contraction twin is shown a higher sensitivity to grain size than that of {1012} extension twin. Annealed Ti with smaller grain size possesses better work hardening. While after rolling process, Ti with lager grain size obtains better work hardening due to higher twin density and lower density of pre-existing dislocations.
Key words: Titanium; twinning; slip; grain size; mechanical property.
Grain size effect on deformation mechanisms and mechanical properties of titanium Z. W. Huang, P. L. Yong, H. Zhou, Y. S. Li* Nano and Heterogeneous Structural Materials Center, School of Materials Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
Abstract The grain size effect on deformation mechanisms and mechanical properties of Ti is investigated by using electron backscattered diffraction technique. Higher twin density and more twin systems are found in Ti with larger grain size after cryogenic rolling process. The percentage of twinned grain increases rapidly first and then become steady until saturation, while the number of twin per grain keeps increasing with the increase of grain size. The generation of {1122} contraction twin is shown a higher sensitivity to grain size than that of {1012} extension twin. Annealed Ti with smaller grain size possesses better work hardening. While after rolling process, Ti with lager grain size obtains better work hardening due to higher twin density and lower density of pre-existing dislocations.
Key words: Titanium; twinning; slip; grain size; mechanical property.
1. Introduction Twinning is important in HCP materials to accommodate deformation strain along the c-axis, since all of the easy slip directions are perpendicular to the c-axis [1-3]. Deformation twin would induce lattice re-orientation of the matrix, while slip is more uniform in strain accommodation. In some cases, {1122} contraction twin (CT) rotates the matrix to a “softer” orientation, leading to better work hardening, while {1012} extension twin (ET) induces a “harder” orientation [4]. Twin boundary could act as barrier to dislocation movement, and has great influence on the flow stress and work hardening behavior of materials [5, 6].
Temperature and strain rate are found to influence the twinning and slip behaviors in HCP materials, e.g., twinning is favored at low temperature and high strain rate while slip is suppressed in these conditions [7]. Besides, grain size is also reported to have influence on the twinning behavior of materials [8-11]. Twins with larger length and thickness were observed in parent grains with larger size, and the twin aspect ratios were also increased with an increase of grain size [12]. Twin volume fraction is found strongly depended on grain size in Ti, while it is almost insensitive to grain size in Mg [12]. Some other studies reported that the twinning probability is independent on the grain size, even the twinning stress decreases with increasing grain size [13, 14]. The increase number of twins per grain could be attributed to the increasing grain boundary area in larger grain [15]. To date, many researchers have investigated the twinning behavior in grains with different size scale via statistical analysis. However, little attention has been paid to the generation of high order twins, e.g., secondary twin, and the variants formation of different twin systems in parent grains with different size scale. Besides, some questions concerning the relationship between deformation mechanisms and the mechanical properties in Ti samples with different grain size remain unanswered. The aim of this research is to investigate the grain size effect on deformation mechanisms and mechanical properties of Ti. Samples were annealed at different temperature to achieve grain size variations. Further rolling treatment was performed at cryogenic temperature with the rolling reduction of 8 %. Electron backscattered diffraction (EBSD) technique was employed to observe microstructures and obtain statistical results. Quasi-static uniaxial tensile test was used to analyze the mechanical properties. 2. Experimental Materials used in this study were commercially pure titanium with chemical composition of (wt. %): Al 0.19, V 0.13, Fe 0.147, Zr 0.098, Cr 0.033, and balance Ti. The as-received Ti was annealed in nitrogen atmosphere at 550℃, 650℃ and 750℃ for 1h respectively, followed by furnace cooling, to obtain samples with different grain sizes and to diminish flaws and residual stress. Before rolling treatment, Ti
samples were polished with abrasive paper to remove oxidations and contaminants on the surface. Samples with different grain size were rolled at liquid nitrogen temperature (LNT) for one pass, with a rolling reduction of 8 %. Before EBSD observation, these annealed and rolled Ti were electro-polished in a mixture of perchloric acid and acetic with 1:9 in volume ratio. EBSD analysis was performed with a FEI Quant 250 field emission scanning electron microscope. The electron beam energy was set to 12 kV. The scanning step size was 0.25 µm and the indexing rate was kept above 85 % to ensure the data veracity. Channel 5 software was used to analysis the EBSD data, for orientation mapping, misorientation distribution analysis and boundary calculation. Uniaxial tensile tests were carried out on a tensile tester, with a strain rate of 3 × 10-3 / s at room temperature, and all of the tests were performed at least three times. 3. Results 3.1. Slip and twinning behaviors The cross-sectional EBSD morphologies of annealed and rolled Ti are shown in Fig. 1. Boundaries with misorientation between 2° to 15° are identified as low angle grain boundaries (LAGBs) and colored by sliver. Those boundaries with misorientation larger than 15° are identified as high angle grain boundaries (HAGBs) and colored by black in all the EBSD images. Grains with misorientations larger than 15° are identified as individual grains, including deformation twins. Since twins would rotate the matrix to different orientations according to definite crystallographic relationship, e.g., 65°/< 1010 > for {1122} and 85°/< 1120 > for {1012} [2], regions in the matrix with corresponding relationship are identified as twins in this work. After annealing at 550 ℃, 650 ℃ and 750 ℃, twinning-free equiaxial grains are introduced in Ti with an average grain size of 4 µm, 10 µm and 50 µm, respectively. After rolling at LNT with the reduction of 8 %, the average grain size of Ti decreases to 1.9 µm, 3.2 µm and 5.1 µm respectively. Note that the average grain size calculated in the research is area average, which is extracted from the EBSD data by using HKL software. After rolling treatment, deformation twins are stimulated to accommodate the strain. Parallel twin lamellae, secondary twin and twin-twin
intersection are detected in parent grains [16, 17]. Fig. 2 gives the texture distributions of annealed and rolled Ti, e.g., (0002) planes and < 1120 > directions. While x and y axs parallel to RD and ND shown in Fig. 1. After annealing, grains are orientated with [0002] axes rotate from ND towards RD, with the deviation angle of ~30°, which reveals typical double peaks texture in Ti [18]. Grain orientations in annealed Ti with different size scale are similar as can be seem from Fig. 2 a-c. After rolling process, density of twins generate in Ti (Fig. 1d-f). Under the effect of twinning, grains are rotated to the orientations with (0002) planes perpendicular to z axis, which parallels to TD (Fig. 2d-f). The distribution of < 1120 > directions becomes more randomly compared with annealed Ti. Misorientation distribution images of annealed and rolled Ti with different grain size are shown in Fig. 3. The bin size used to generate the figure is 1°. No obvious misorientation peak is found in annealed Ti, i.e., black histograms in Fig. 3 a-c. After rolling treatment, only one obvious misorientation peak around 65° is detected in Ti with the average grain size of 4 µm (Fig. 3a). It is corresponding to {1122} CT in HCP material, which rotates the matrix by 65° along < 1010 > [19]. With the grain size increasing, other misorientation peaks around 77° and 85° are found in Ti as shown in Fig. 3b and c, and they are corresponding to {1124} CT and {1012} ET respectively [18]. The misorientation peak of {1122} CT is obviously higher than that of {1124} CT and {1012} ET. While the intensity of {1124} CT and {1012} ET peaks is nearly equivalent. Results reveal that the number of twinning system increases with increasing grain size, and {1122} CT is the dominating twinning system in rolled Ti when deformed at cryogenic temperature [18].
Fig. 1 Cross-sectional EBSD images of annealed Ti with the grain size of (a) 4 µm, (b) 10 µm, (c) 50 µm, and rolled Ti with the grain size of (d) 4 µm, (e) 10 µm, (f) 50 µm.
Fig. 2 Texture distributions of annealed Ti with the grain size of (a) 4 µm, (b) 10 µm, (c) 50 µm, and rolled Ti with the grain size of (d) 4 µm, (e) 10 µm, (f) 50 µm.
Fig. 4 gives the boundary fraction calculation results of annealed and rolled Ti, including LAGBs, HAGBs and twin boundaries. The LAGB and HAGB percentage
in annealed Ti with different grain size is almost equivalent (Fig. 4a), with a value of 10.8 ± 0.4 % and 89.2 ± 0.4 %, respectively. After rolling process, the LAGB percentage of Ti with the average grain size of 4 µm increases rapidly to 25.0 %, with an increment of 13.8 % (Fig. 4b). It implies a severe dislocation accumulation in Ti with small grain size during rolling process [20]. While a relatively low twin boundary percentage (15.4 %) is detected in the sample. As the average grain size increases to 10 µm and 50 µm, the LAGB percentage decreases to 14.9 % and 13.7 %, and the twin boundary percentage increases to 28.3 % and 30.0 % respectively. It proves the concept that twinning is favored in Ti with larger grain size, which is consistent with previous investigations [12].
Fig. 3 Misorientation distributions of annealed Ti (black histograms) and rolled Ti (red histograms) with the average grain size of (a) 4 µm, (b) 10 µm, (c) 50 µm.
Fig. 4 (a) LAGB and HAGB percentage in annealed Ti and (b) LAGB, TB and HAGB percentage in LNT-rolled Ti with different grain size.
3.2. Twinning variations Grain size effect on the generation of primary, secondary twin and the activation of different twin systems in Ti is investigated, and the statistical results are shown in Fig. 5. Parent grains with size scale range from 1 µm to 80 µm are taken into consideration in this research. Fig. 5a gives the percentage of parent grain containing primary and secondary twin. With an increase of grain size, the percentage of twinned grain increases rapidly first, then reach a critical value and become steady until saturation. The critical grain size for primary twin is ~10 µm, which indicates that primary twins generate in over 90 % of the grains with size no less than 10 µm. Besides, the critical grain size for secondary twins is ~17 µm, and over 70 % of the grains with larger size contain secondary twins. Since the twin size strongly depends on the grain size, larger parent grain is required to generate high order twin, e.g., secondary twin. Fig. 5b gives the number of twins per grain in parent grains with different size. The number of twin increases from no more than 2 twins in parent grain with the size of 1 µm to over 16 twins in parent grain with the size of ~75 µm, and this tendency is consistent with previous investigation [12]. Similarly, the number of primary and
secondary twin increases with increasing grain size. While the number of primary twin per grain is larger than that of secondary twin in parent grain with the same size. Fig. 5c gives the number of twin variants per grain with different grain size. Four common twin systems are taken into consideration in the research, e.g., {1121} , {1012} ETs and {1122}, {1124} CTs. Results show that the number of twin variant per grain increases with an increase of grain size. The number of {1122} CT is the highest in parent grain with the same size. It reveals that {1122} CT is the dominant twinning system in Ti when deformed at cryogenic temperature [18], and this is consistent with the misorientation peak intensity shown in Fig. 3. The number of {1012} ET is the second highest, while a few {1121} ET and {1124} CT is detected. Notice that the slope of {1122} CT is higher than that of {1012} ET, which implies that the generation of {1122} CT is more sensitive to grain size. The slopes of {1121} ET and {1124} CT are the lowest in the study.
Fig. 5 Distributions of (a) percentage of parent grain containing primary twin / secondary twin
among all the detected grains, (b) number of all twin / primary twin / secondary twin per grain, and (c) number of different twin variant per grain in Ti, with the increase of grain size.
As discussed, the grain size effect on the generation of different twin variants is different. The total number fraction of {1121} ET and {1124} CT is calculated smaller than 5 % in this research, and these two variants are not taken into further discussion. For the dominant {1122} CT and {1012} ET, the slope of {1122} CT is higher, indicating a higher sensitivity to the grain size. Fig. 6 gives a typical morphology of areas containing {1122} CT and {1012} ET in rolled Ti. Results show that {1012} ETs are with prism structure and take up a large volume fraction of the parent grain. No more than two twins can be observed in a grain simultaneously. While {1122} CTs show lamellae structure, and up to 4 twins can be found in a grain. It is because the twinning shear of {1012} ET (0.175) is smaller than that of {1122} CT (0.218), and a larger volume fraction is required for {1012} ET to accommodate the same deformation strain as {1122} CT [1, 18]. The formation of {1012} ET takes up a large volume fraction of the parent grain, and the generation of subsequent variant becomes difficult due to higher twinning stress in smaller grain.
Fig. 6 EBSD images of area containing (a) {1122} CTs and (b) {1012} ETs in LNT-rolled Ti samples with the average grain size of 4 µm.
3.3. Mechanical properties Fig. 7 gives the typical tensile test curves of annealed and rolled Ti, and the corresponding statistical results are shown in table 1. Annealed and rolled Ti samples
with different grain size are coded as 1 # to 6 #. Results reveal that annealed Ti with the average grain size of 4 µm has the highest strength, e.g., yield stress ( MPa) and ultimate tensile stress ( (
� ,
381
, 450 MPa), and the largest uniform elongation
, 13.3 %). With the increase of grain size, the yield stress and uniform elongation
decrease simultaneously, which is consistent with previous investigation [21]. After rolling process, Ti with smaller grain size possess higher strength but with lower tensile ductility. Fig. 7b gives the work hardening curves and the true strain-stress curves of annealed and rolled Ti. The work hardening rate (θ) is given by θ = ∂σ/ ∂ε, where σ is the true stress and ε is the true strain of the sample. Results show that smaller grain size leads to better work hardening in annealed Ti. On the contrary, better work hardening is detected in Ti with larger grain size after rolling.
Fig. 7 (a) Tensile engineering strain-stress curves of annealed and rolled Ti samples with different grain size, and (b) corresponding true strain-stress curves and work hardening rate curves. Table 1 Mechanical property statistic of annealed and rolled Ti. Sample 1# 2# 3# 4# 5# 6# *
: yield stress;
Engineering stress/strain /MPa /MPa ! "#/% 381 310 249 525 505 483
450 405 268 605 575 556
0.133 0.127 0.113 0.021 0.041 0.050
: ultimate tensile stress;
True stress/strain /MPa 385 313 251 552 507 493
/MPa 515 460 425 610 600 585
!
"# /%
0.138 0.132 0.118 0.022 0.042 0.051
: uniform elongation.
Notice that for rolled Ti, the strain path changes from rolling (plane strain
deformation) to tension during the test, which is an orthogonal strain path change. Due to various strain states, the generation of different slip systems may have influence on the yield points of Ti samples, e.g., lower mobile dislocation density. Hence, Schmid law is used to study the slip activities of Ti samples under different strain path. Fig. 8 and Fig. 9 give the Schmid factor distributions of Ti samples during annealing and sequential rolling treatments. All the four slip systems, i.e., basal, prismatic, pyramidal and
Fig. 8 Schimid factor distributions of different slip systems in (a-d) 1# annealed Ti, (e-h) 2# annealed Ti, (i-l) 3# annealed Ti during rolling treatment, the loading stress parallels to ND. Percentage of pixels with hard orientations (0-0.3), soft orientations (0.3-0.5) and the average Schmid factors are given.
After rolling treatment, Schmid factor distributions of rolled Ti during tensile test are shown in Fig. 9. Results show that pyramidal slip with the average Schmid factor of 0.392 is the most possible to generate, while basal sip with the average Schmid factor of 0.229 is the hardest to be stimulated, which is distinctly different from Ti during rolling treatment. It is because the strain path changes significantly from plane strain to tensile strain as discussed, and which is beneficial to stimulate pyramidal slip. It is known that Schmid factor denotes the resolved shear stress (RSS) of applied stress (
$%%& '( )
on corresponding slip planes. On the contrary, if the critical resolved
shear stress (CRSS) and Schmid factors of the slip systems are known, the
$%%& '(
needed to stimulate the dislocation can be calculated by: $%%& '(
=
)*++ /,
(1)
Where m is the Schmid factor of corresponding slip system. In this study, the average Schmid factors of different slip systems are calculated by using HKL software. The CRSS requires to generate basal slip, prismatic slip and pyramidal slip are calculated as: 150 MPa, 30 MPa and 120 MPa respectively [23]. Hence, the
$%%& '(
needed to
activate slip systems in Ti during rolling and tensile treatments can be calculated, and results are shown in table 2.
Fig. 9 Schimid factor distributions of different slip systems in (a-d) 4# rolled Ti, (e-h) 5# rolled Ti, (i-l) 6# rolled Ti during tensile process, the loading stress parallels to RD. Percentage of pixels
with hard orientations (0-0.3), soft orientations (0.3-0.5) and the average Schmid factors are given.
During rolling process, the
$%%& '(
requires to generate prismatic slip is
the lowest in Ti samples, in spite of corresponding low Schmid factor. Hence, prismatic dislocation generates and accumulates during rolling treatment, resulting in the increase of LAGBs (Fig. 4). During tensile process, the texture is favorable to generate prismatic slip, and the
$%%& '(
requires to stimulate the dislocation is
obviously lower than that to generate other dislocations. That is to say, prismatic slip is the dominant slip system in Ti during rolling and tensile treatment, and the generation of dislocation becomes easier when deformed along tensile direction. Hence, strength increment of the yield points may not be attributed to the lower mobile dislocation density, and could be relative to dislocation strengthening and grain boundary strengthening.
Table 2 Applied stress (MPa) needed to generate different slip systems in Ti during rolling and tensile processes. Rolling process 1# Annealed Ti 2# Annealed Ti 3# Annealed Ti
Basal 373 374 386
Prismatic 151 210 214
Pyramidal 344 370 379
Pyramidal 306 317 326
Tensile process 4# Rolled Ti 5# Rolled Ti 6# Rolled Ti
Basal 655 711 761
Prismatic 78 81 83
After yielding, with the increase of flow stress, slip and twinning are triggered to accommodate the local strain and contribute to work hardening. With the tensile process continues, dislocation and twinning behaviors may induce dynamic softening in Ti. In this research, grain size variation leads to different degrees of dislocation accumulation and twin boundary fraction in Ti (Fig. 4b), thus influence the dynamic softening process during tensile test. Qin et al. [23] reported that the initiation of
twinning and dynamic softening, e.g., dynamic recrystallization (DRX), can be detected from the following condition: -
-.
/−
-1
-.
2=0
(2)
From the equation, three points of inflection in each of the curves can be derived, and they are corresponding to two minima and one maximum [24]. The first minimum point is associated with the initiation of twinning, and the second relates to the initiation of dynamic recrystallization. While the maximum point indicates a decrease in the twinning rate. Besides to twinning and DRX, dislocation activities could be another influence factor of dynamic softening, since dislocation recovery may occurs with continues dislocation accumulation. The work hardening derivative on true stress (− 4564 ) curves of annealed and rolled Ti are shown in Fig. 10. The first minimum point is not prominent in annealed Ti with the average grain size of 4 µm and 10 µm (Fig. 10a, b). While the critical stress for the second point is lower in Ti with larger grain size, e.g., 480 MPa for Ti with the average grain size of 10 µm and 530 MPa for Ti with the average grain size of 4 µm. For Ti with the average grain size of 50 µm, twinning occurs when the stress reaches 380 MPa (Fig. 10c). As the stress increases to 440 MPa, dynamic softening happens in Ti. This critical stress for dynamic softening is the lowest among all the annealed samples. After rolling treatment, the two minima points are obvious in Ti (Fig. 10d-f). With the grain size increase, the critical stress for twinning decreases from 608 MPa to 564 MPa, and from 627 MPa to 590 MPa for dynamic softening. It reveals that both twinning and dynamic softening become easier during tensile test in Ti with larger grain size.
Fig. 10 Work hardening derivative on true stress curves of (a-c) anneal Ti and (d-f) rolled Ti with different grain size. The upward and the downward black arrows represent the first and the second minima points respectively.
4. Discussion In HCP materials, the critical resolved shear stress for twinning decreases with the increase of grain size [1]. It is widely reported that twin boundary could act as barrier to dislocation movement, thus resulting in higher strength [25, 26]. In order to investigate the contribution of twin boundary to the strength increment of Ti, Hall-Petch relationship is considered in this research. According to the relationship, grain boundary strengthening of materials can be calculated by: σ= Where
8
8
+ :; <
=6 >
(3)
is the friction stress and k is a constant. Assuming that pre-existing
dislocations are recovered and annihilated after annealing treatment, the yield stress of annealed Ti primarily attributes to grain boundary strengthening. The yield stress of 1#-3# annealed Ti with average grain size of 4 µm, 10 µm and 50 µm are 381 MPa, 310 MPa and 249 MPa respectively (table 1). Hence,
8
and k are calculated 196
MPa and 0.368 MPam1/2 as shown in Fig. 11. After rolling treatment, average grain size of 4#-6# rolled Ti decreases to 1.9 µm, 3.2 µm and 5.1 µm as discussed. According to Hall-Petch relationship, the yield stress increases to 462 MPa, 402 MPa and 359 MPa, with the increment of 81 MPa, 92 MPa and 110 MPa respectively.
Higher yield stress increment of Ti with larger grain size after rolling treatment could be attributed to higher twin volume fraction as shown in Fig. 4. Besides, dislocation accumulation contributes to the additional stress increment of Ti before yielding. Generally, the Hall-Petch fitting is fine in this research, but the resistance of twin boundaries to dislocations is not the same as that of random HAGBs. However, since little data is available, only grain size including twin size is fitted using Hall-Petch relationship.
Fig. 11 Hall-Petch relationship of annealed Ti
In addition to the strength increment, higher twin density also contributes to better work hardening. Assuming that the imposed deformation strain on Ti is equivalent during rolling process. Either twinning or slip is stimulated to accommodate the strain. Twinning is active in Ti with larger grain size as discussed, and high density of twin accommodates a larger portion of the strain. Thus, relatively lower density of dislocation generates to release the strain. It results in higher twin boundary percentage and lower LAGB percentage in Ti with larger grain size (Fig. 4b). Firstly, because of low density of pre-existing dislocations, rolled Ti with larger grain size possess better work hardening during tensile test. On the contrary, twinning is hard to generate in Ti with smaller grains because of higher twinning stress. Slip is stimulated to accommodate the strain, resulting in high density of pre-existing dislocations and worse work hardening. Secondly, twinning could rotate the parent grain to the orientation in favor of slip. Therefore, rolled Ti with higher twin boundary fraction possess better work hardening.
As is known, dynamic hardening and dynamic softening exist simultaneously during tensile process. The former relates to slip and the latter derives from twinning, slip and continuous DRX [9]. For annealed Ti with small grain size (4 µm), slip is the dominating deformation mechanism during tensile test. Dislocation generates and tangles with increasing stress, areas containing high dislocation density could serve as site for continuous DRX because of high stored energy [27]. Since certain extent of dislocation accumulation is required to trigger continuous DRX and dislocation recovery, critical stress for the second minimum point is relatively higher as shown in Fig. 10a. With the grain size increase to 10 µm, twinning becomes easier in Ti. However, since the twin volume fraction is still in low level, the first minimum point for twinning is not prominent as shown in Fig. 10b. Notice that the slope of the curve changes with the increase of stress, therefore the curve can be divided into three stages: stage 1, dislocation tangle; stage 2, twinning occurs; stage 3, decrease of twinning rate. As the grain size keep increasing, higher twin volume fraction is introduced, and the first minimum point for twinning becomes obvious. Yan et al. [27] investigated that twin boundary could serve as site for DRX because of high stored energy, thus promote the occurrence of DRX. Hence, dynamic softening becomes easier in Ti with larger grain size, leads to lower stress for the second minimum point. After rolling treatment, high dislocation density generates in Ti with small grain size (4 µm), with the LAGB percentage of 25.0 % as shown in Fig. 4b. Dislocation accumulation can not only be the site for continuous DRX, but also promote twinning due to high stored energy [2]. Therefore, the first minimum point for twinning appears when the stress reaches 608 MPa (Fig. 10d). Besides, twin boundary fraction increases with increasing grain size. It leads to the lower critical stress to stimulate twinning and dynamic softening during tensile process. 5. Conclusion Ti samples with different grain size are studied to investigate the grain size effect on their deformation mechanisms and mechanical properties, and following conclusions can be drawn: (1) Twin boundary fraction and the number of active twinning system increase with
the increase of grain size in Ti during rolling treatment. While higher dislocation density is detected in Ti with smaller grain size. (2) The percentage of parent grain containing primary and secondary twin increases rapidly first and then becomes steady with the increase of grain size. The critical grain size for the percentage increment of primary and secondary twin is 10 µm and 17 µm respectively. Besides, the twin number increment of primary twin is larger than that of secondary twin with increasing grain size. (3) The twin number per grain of {1122} CT is more sensitive to grain size than that of {1012} ET, which is related to the twinning shear and twin morphology. The generation of {1012} ET would consume lager volume fraction of parent grain than that of {1122} CT, thus hinder the formation of subsequent twin. (4) Annealed Ti with smaller grain size possess higher strength, larger uniform elongation and better work hardening. A larger strength increment is calculated in Ti with larger grain size after rolling, because of higher twin boundary fraction. Besides, high twin density and low pre-existing dislocations accumulation contribute to better work hardening of rolled Ti with large grain size.
Acknowledgements This work was supported by the National Key R&D Program of China (2017YFA0204403), National Natural Science Foundation of China (51741106), Natural Science Foundation of Jiangsu Province (BK20191292), the Fundamental Research Funds for the Central Universities (30919011256), the Jiangsu Key Laboratory of Advanced Micro & Nano Materials and Technology, and Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX18_0415). EBSD was performed in the Materials Characterization and Research Center of the Nanjing University of Science and Technology.
Data availability The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.
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Authors' contributions: ZW Huang performed the experiment and analysis; PL Yong helped with the sample preparation; H Zhou and YS Li proposed the idea, designed the experiment and responsible for the paper.
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: