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Coupling effect of second phase and phase interface on deformation behaviours in microscale Ti-55531 pillars
Journal of Alloys and Compounds 820 (2020) 153421
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Coupling effect of second phase and phase interface on deformation behaviours in microscale Ti-55531 pillars Wenjuan Kou, Qiaoyan Sun*, Lin Xiao**, Jun Sun State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 7 August 2019 Received in revised form 9 December 2019 Accepted 16 December 2019 Available online xxx
The metastable-b Ti-55531 alloys with different second phases were chosen to investigate coupling effect of second phase and interface as well as the dislocation interaction details under uniaxial compression. In Ti-55531 alloy, nanoscale u phase was acquired by solution treatment, which was coherent with the b matrix. The orientation relationship between hexagonal u and bcc b lattice was (0001)u//(111)b and [1120]u//[110]b. Sub-microscale a phase was acquired by ageing process, following the Burgers orientation relationship (BOR), {110}b//{0001}a and <111>b//<1120>a. The characters of mechanical behaviors and deformation microstructures in this alloy have been analyzed by combining the results from uniaxial compression, scanning electron microscopy (SEM), transmission electron microscopy (TEM) and highresolution TEM. Ti-55531 alloy micropillars with deformable a phase show great plastic stability and high strength, which are attributed to the deformable a phase and the interaction between the dislocations and the high-density a/b interface. However, Ti-55531 alloy micropillars with nanoscale u phase exhibit size effect and poor plastic stability. The deformation mechanism of the Ti-55531 pillars with u phase is dislocation shearing the u phase, which will cause the u/b phase transformation. The u-free channels result in the collective movement of dislocations, performed as the strain bursts in the stressstrain curves. But the dislocation slip between the a phase and the b matrix follows a harmony slip mode, which is similar to “slip relay” behaviour. The results reveal that tuning the morphology of phase interface and the density of second phase to govern the activation, multiplication and movement of dislocation is an effective method to tailor the strength and plastic deformation of materials. The deformation model between the dislocations and the phase interface has great significance to the design of the high performance materials by optimizing the microstructures. © 2019 Elsevier B.V. All rights reserved.
Keywords: Ti alloy Phase interface Microstructure Mechanical properties Microscale
1. Introduction Metals have been the most important materials for human beings in thousands of years. Finding the balance between strength and plasticity is the most effective way to maximize the mechanical properties of material [1]. The traditional strengthening methods were work hardening, solid-solution strengthening, interface strengthening, precipitation hardening and so on [2,3]. The interfaces play important roles in crystalline plasticity as they often serve as obstacles for dislocation motion, as well as dislocation
* Corresponding author. State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, PR China. ** Corresponding author. State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, PR China. E-mail addresses: [email protected] (Q. Sun), [email protected] (L. Xiao). https://doi.org/10.1016/j.jallcom.2019.153421 0925-8388/© 2019 Elsevier B.V. All rights reserved.
sources/sinks [4]. For example, nanocrystalline materials are structurally characterized by a large volume fraction of grain boundaries, which may significantly increase the strength in comparison with conventional coarse-grained polycrystalline materials, but the plastic deformation will be limited by the decreasing of grain size [4,5]. Compared to the classical grain boundaries, introducing the phase interface is another efficient method to enhance the mechanical properties of alloy, because a uniform distribution of the second phase impede dislocation motion which strengthens the alloy directly [2,3]. Usually, the second phases are nanometer scale, and the corresponding strengthening mechanisms can be divided into two categories, the dislocation shearing mechanism and the Orowan dislocation bypassing mechanism, depending on the interaction between moving dislocations and second phases [6,7]. Most of high-performance metallic materials, including Al alloys, Mg alloys, stainless steels, and Ni superalloys, all contain a uniform
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microstructure of the diverse second-phase particles distributed in matrix [8e13]. Magnesium alloys have shown that nano/micro– precipitates can act as sites and paths for void nucleation, crack initiation and subsequent crack propagation during spall failure [14]. The coherent precipitation of cuboidal L12-g’ particles in Nibased superalloys are responsible for the necessary strength at much higher temperatures near to the melting point [15,16]. In addition, the enhancement effect increases with the increase of the second phase content. However, when the content increases to a much higher value, it becomes difficult to start the internal dislocation of the material due to lattice distortion, stress field and other effects [17]. The dislocations are locked at the phase interface and could not be activated and move. The poor strain hardening rate (SHR) of the alloy containing second phase has proved that the locked dislocations at the interface are associated with plastic localization [18,19]. So the nanoscale second phase strengthening has an upper bound. As we known, the strength of crystalline materials is principally determined by the limit to elastic deformation, with subsequent plastic deformation occurring by the nucleation and propagation of dislocations [20]. The interfaces are not only the barriers to dislocation, but also the sources or storage sites for dislocation. For example, A. Misra [21] found that the slip was transferred from gþg0 phase to the b phase via a gþg’ phase dislocation gliding into the semi-coherent interface and converted into a glissile dislocation in the b phase. K.S. Ng [22] found that coating aluminum micro-columns with tungsten could eliminate the strain bursts and significantly increased the strain-hardening rate, because the interface of coating trapped dislocations inside the crystals, thus raising the stored dislocation density by up to three orders of magnitude. So the interfaces not only trap the mobile dislocations but also exist as the sources of dislocation nucleation. If the space between the interfaces is large enough, dislocation movement may transmit cross the interface and dislocation can store and propagate in the space, which ensures the good plastic deformation capability. At the same time, keeping the large volume fraction of interfaces would guarantee the excellent strength of alloys. The metastable b titanium alloys, as the next-generation highperformance materials, their mechanical properties are strongly dependent on the microstructural characteristics [23e26], therefore the second phase in b matrix has been a topic of intensive studies. Tuning the second phase may have a great chance to get a good match between the strength and plasticity. In this study, highdensity a/b interface and discrete nanoscale u/b phase interface were acquired by different heat treatments to investigate the optimizing of strengthening and plasticity by different interface structures. It is worth noticing that the properties of the metastable b-Ti alloys are almost tested from the polycrystalline bulk materials, and the effect of grain boundaries cannot be excluded [27]. Precise mechanistic analysis using nanoindenter becomes widely used to investigate the local area deformation characters [28,29]. It is thought that small-scale experiments on a localized, confined area are required to understand of the fundamental mechanisms on the level of the individual microstructural constituents. Therefore, the micropillar compression technique was adopted to isolating individual microstructural units and selecting particular slip systems for investigation, which is difficult to achieve by compression of bulk samples. In this work, local deformation mechanisms in twophase Ti alloys were investigated by the micropillar compression focusing on coupling effect of second phase and phase interface change local slip behaviour as well as work hardening in compression. This work provides the basis for further understanding of fundamentals on nanomechanics of alloy pillars with specific second phase.
2. Experimental procedures A commercial metastable b-Ti alloy, Tie5Ale5Moe5Ve3Cre1Zr (Ti-55531) bulk was chosen in this work. Two Ti-55531 alloy bulks with 6 mm in diameter and 4 mm in height, were cut using spark machine from the hot rolled bar, and then solution-treated at 950 C for 24 h in vacuum followed by quenching to room temperature in water. The metastable b phase was retained by quenching above the b transus temperature. The achieved b grain size was in the range of 0.5e1 mm. The grain size was measured by Nano Measurer software. One of the bulks needed a further isothermal vacuum annealing, performed at 300 C for 20 h to form a large number of isothermal u phase, which can become nucleus of the stable a phase nucleation [30e32]. Then the annealing temperature was further increased to 650 C for 15 h to dissolute the remained u phase and promote the growth of a phase by clustering different a variants into self-accommodating morphologies [31]. Therefore, one b Ti-55531 alloy bulk with nanoscale u phase and the other one with high density of sub-microscale a phase were produced. The square bulk was mechanically and electrochemically polished before fabricating into micropillars. The grain orientation was determined via electron backscattered diffraction (EBSD). For both of the Ti-55531 alloy bulks, grains oriented to <101>b were selected to fabricate micropillars using Focus Ion Beam (FIB) technique, as shown in Fig. 1(a) and (b). The SEM microstructure of the aged (at 650 C) Ti-55531 alloy was shown in Fig. 1(c), which exhibited high-density a/b interface. A group of single-crystal micropillars were fabricated using the FEI Helios operated at an ion beam voltage of 30 kV with a variety of currents, as shown in Fig. 1(d). The micropillar diameter, ranges from 150 nm to 2.5 mm, with an aspect ratio of ~2.5. The taper of the micropillars is between 6 and 2 . Three to five samples were prepared each size. Uniaxial compression experiments were conducted in Hysitron Ti-950 nanoindenter with a 10 mm flat punch diamond tip at a constant nominal strain rate of 1 103/s. The loading mode was displacement control. The loading-displacement dates would be acquired after compression. The post-compression morphology of the micropillars was observed with SEM. All TEM specimens were prepared by lifting out technique using a nanomanipulator (AutoProbe 200, Omniprobe, Inc.) and transferring them onto Cu grids. The micropillar samples were then thinned to the electron-transparent thickness (～100 nm) by using the FIB. 3. Results 3.1. Mechanical behavior of uniaxial compression Typical stressestrain curves of the solution-treated and the aged (at 650 C) Ti-55531 alloy micropillars with various diameters compressed along <101>b orientation are shown in Fig. 2(a) and (c). The yield strength is defined as the flow stress of the micropillar at 0.2% engineering strain. For the solution-treated Ti-55531 alloy micropillars, the strain bursts are more and more obvious with the decrease of diameter, as shown in Fig. 2(a). The relevant yield strength increases from 0.9 GPa to 1.5 GPa, showing the “smaller is stronger” phenomenon, as shown in Fig. 2(b). The power-law fitting gives a relationship between the yield strength and diameter, s~Dm , the exponent m is 0.335. For the aged Ti-55531 alloy micropillars, the stressestrain curves are smooth and continuous, as shown in Fig. 2(c). The yield strength is about 1.5 GPa, regardless of the pillar sizes, as shown in Fig. 2(d). The exponent m is 0.06. The results indicate that the size effect of the aged micropillars is much weaker than that of the solution-treated micropillars. On a close examination, the stress-strain curves of the aged micropillars show a smooth and stable plastic deformation behavior, which is much
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Fig. 1. (a) EBSD map of the solution-treated Ti-55531 alloy bulk specimen before FIB milling (the white lines indicate location marks), (b) EBSD map of the aged (at 650 C) Ti-55531 alloy bulk specimen before FIB milling, (c) Typical SEM microstructure of the aged (at 650 C) Ti-55531 alloy, (d) Typical SEM morphology of the micropillar.
Fig. 2. Compressive behaviors of the Ti55531 micropillars (a) The engineering stressestrain curves and (b) yield strengths (at 0.2% plastic strain) versus pillar diameter of the solution-treated Ti-55531 alloy micropillars, (c) The engineering stressestrain curves and (d) yield strengths (at 0.2% plastic strain) versus pillar diameter of the aged Ti-55531 alloy micropillars.
similar with the bulk sample [33]. So the aged Ti-55531 micropillars exhibit an excellent combination of high strength and stable plasticity. The strain hardening rate (SHR) is quantified in Fig. 3 as a function of pillar diameter. Due to the displacement bursts during the stressestrain response of the micropillars, SHR is defined as the
slope between the true stressestrain data values at 3% and 10% strain. This definition is similar to that used in an analogous study [34,35]. The SHR of the aged micropillars is higher than that of the solution-treated micropillars. An increase in SHR of the solutiontreated micropillars is observed to correlate with decreasing diameter. However, the SHR of the aged micropillars slightly
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observed on the surfaces instead of the significant slip steps in solution-treated micropillars, as indicated by the red arrows in Fig. 4(e) and (f). At the same time, many fine slip steps are visible on the sides of micropillars. Based on the analysis of slip traces, {112}b <111>b slip system is activated in the aged Ti-55531 alloy micropillars. 3.3. Deformation mechanisms of the solution-treated and aged (at 650 C) Ti-55531 alloy micropillars
Fig. 3. The SHR for the solution-treated (red points) and the aged (black points) Ti55531 alloy micropillars with different diameters. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
increases with the diameter. 3.2. Deformation modes of solution-treated and aged (at 650 C) Ti55531 alloy micropillars Fig. 4(a)e(c) show SEM images of the deformed solution-treated and aged Ti-55531 alloy micropillars, respectively. A group of parallel slip bands and several large slip steps are observed on the surface of the solution-treated Ti-55531 alloy micropillar, as indicated by the white dash lines in Fig. 4(a)e(c). On a close examination, only one slip system is activated in the solution-treated micropillars. The angle between the slip plane and the top surface of pillar ({101}b) is 53 , which indicates that the {112}b <111>b slip system is activated in the solution-treated micropillars, as shown in Fig. 4(c). The same slip system is observed in other b titanium alloys [36e38]. For the aged Ti-55531 alloy micropillars, tortuous slip traces are
3.3.1. Microstructure of the micropillars before deformation Fig. 5(a) shows typical TEM microstructure of the solutiontreated Ti-55531 alloy micropillar before deformation. The selected area electron diffraction (SAED) pattern analysis along the <011>b zone axis of b matrix shows that the primary components in the solution-treated Ti-55531 alloy includes the b matrix and the u phase. Nanoscale u phase homogeneously distributes in the b matrix. These u phase are produced through athermal transformation from the b to the u during water quenching. The size of u phase is only several nanometers. Fig. 5(b)-(d) shows typical TEM microstructure of the aged Ti55531 alloy micropillar before deformation. High density of a phase is acquired in the b matrix. The size of a phase is 100e300 nm, which is much larger than that of u phase. The b matrix has a common b-{110} pole with the a-{0001} pole. The a phase and the b matrix own the following Burgers orientation relationship: {110}b//{0001}a and <111>b//<1120>a [39e41]. The a phase is short rod-like and uniformly distributes in the b matrix, as shown in Fig. 5(b)-(c). Fig. 5(d) shows that the boundaries of a phase are clear and smooth. The volume fraction of a phase is about 40%, obtained from the SEM images by the Photoshop software. The size of a/b interface was much larger. 3.3.2. Microstructure in the deformed micropillars Fig. 6 shows the TEM micrograph of the ~20% deformed solution-treated Ti-55531 alloy micropillar. The slip traces in the TEM image confirm that the {112}b <111>b slip system is activated, as shown in Fig. 6(a). A set of parallel slip lines are observed inside
Fig. 4. SEM morphology of the deformed micropillars with different diameters (a)-(c) the deformed solution-treated Ti-55531 alloy micropillars, (d)-(f) the deformed aged Ti-55531 alloy micropillars.
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Fig. 5. Microstructures of the micropillars before deformation. (a) the distribution of the u phase in the b matrix, (b) the distribution of a phase in the b matrix, (c) the bright-field image and (d) the dark-field image of a phase.
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amount of u2 has little change in the same region along slip, as shown in Fig. 6(d)-(e). These observations suggest that a channel depleted of the u1 phase is formed along the slip line. Thus, the absence of u1 inside slip traces indicates a phase transformation from the u1 to the b matrix under compressive stress. The similar results are also observed in some other b-Ti alloys [36,42]. Therefore, the deformation mechanisms in the solution-treated Ti-55531 alloy micropillar include dislocation interaction with the u phase and the stress-induced phase transformation along slip planes. Fig. 7 shows the TEM micrographs of the deformed aged (at 650 C) Ti-55531 alloy micropillar. No slip bands can be distinguished and the boundaries of some a phase are blurry and tortuous. It is quite difficult to recognize the interface between the a phase and the b matrix, as shown in the magnified area in Fig. 7(a). The Fig. 7(b)-(c) show the bright-field and dark-field images of the deformed a phase, respectively. The slip traces can be found in some a phase and even some slip steps are observed in the interface between the a phase and the b matrix, as indicated by the red narrows in Fig. 7(c)-(d). Some parallel dislocations are stored in the a phase (Fig. 7(e)), which will introduce working hardening. Fig. 8(a) shows the high-resolution transmission electron microscope (HRTEM) image of the a/b interface. There are no obvious dislocations pile up near the a/b interface, and the dislocations can be observed in the a phase, as shown in Fig. 8(b). This result indicates that the a phase and the b matrix undertake the plasticity simultaneously. 4. Discussion
the micropillar, as indicated by the white dash arrows in Fig. 6(b). Further observation of Fig. 6(c) shows a bright-field image of one slip trace and the inset of in Fig. 6(c) is the corresponding diffraction pattern, which shows weak diffraction intensity of the u1, and a normal diffraction intensity of the u2, as marked by the two white circles. The related dark-field TEM images using the u1 and the u2 reflections show that two u variants have the same amount and uniformly disperse throughout the b matrix in the non-slip region, but the u1 precipitates almost disappear along slip traces and the
4.1. The interaction between the dislocation and u/b interface The yield strength of the solution-treated Ti-55531 alloy single crystal micropillar increases with the decrease of pillar diameter in a power law of s fDm . The strengthening exponent, m, is 0.335. It’s well known that when the pillars are composed of the secondary particles and the matrix, interactions between the dislocations and secondary particles weaken the size effect [27,43e45]. In this work, it can be attributed to the formation of nanoscale u
Fig. 6. Microstructures in the deformed solution-treated Ti-55531 alloy micropillar. (a) the whole morphology of the deformed micropillar, (b) slip traces in the pillar, (c) the brightfield image of the slip line, the related dark-field TEM images of (d) the u1 and (e) the u2.
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Fig. 7. TEM microstructures in the deformed aged (at 650 C) Ti-55531 alloy micropillar. (a) the deformed a phase in the b matrix, (b) the bright-field image and (c) the dark-field image of the a phase, (d) slip step in the a phase, (e) dislocations stored in the a phase.
Fig. 8. (a)HRTEM images of the deformed a/b interface, (b) Inverse Fourier transform of Fig. 8(a).
phase. An interface and u phase are introduced into pillars to modify the size effect on strength. As mentioned above, the deformation-induced microstructure evolution reveals that the phase transformation from the u1 to the b matrix occurred under uniaxial compression. The orientation relationship between hexagonal u and body-centered cubic (bcc) b lattice is (0001)u//(111)b and [1120]u//[110]b [46]. It reveals that the prismatic slip plane {1100}u of the u phase is parallel to the {112}b slip plane of the b matrix. Based on the slip trace analysis, {112}b<111>b slip system is activated in the b matrix. Taking into account the relatively low misfit between the lattices and the coherent character of the u/b interface [47], such a coherence of the slip planes in b and u facilitates the slip transfer from the {112}b planes onto the {1100}u planes. The dissociation of dislocation lead to the stress-induced phase transformation. The motion of a perfect 1/2 <111>b dislocation on the {112}b slip plane is blocked by the u phase and dissociates into three partials, b1 ¼ 1/12 <111>b, b2 ¼ 1/3 <111>b and b3 ¼ 1/12 <111>b, on three consecutive {112} b planes [36]. The movement of these dislocation partials causes the u phase back into the b phase. The phase transformation phenomenon follows the traditional deformation mechanism, dislocation
shearing the second phase. Among the four possible u variants, only one variant’s [0001]u direction parallel to a particular [111]b direction [41,48]. Therefore, only one u variant can transform back to the b matrix. And the other three u variants remain unchanged under the same stress condition. The dislocations-u interaction suggests that the dislocations shear the u phase along the {112}b//{1100}u slip planes, forming channels that are devoid of the u1 phase, as indicated in Fig. 9(b). The channels cause that the resistance against further dislocation movement reduced, so the dislocation slip are localized. The dislocation motion along slip planes results in the formation of dislocation channels and the plastic flow localization, which would introduce the strain bursts. The SHR of the solution-treated micropillars verifies that the model of dislocation motion is dislocation slip localized without multiplication or accumulation so that the usual mean-field conditions for forest hardening are destroyed [20,34].
4.2. The strengthening by the nanoscale u phase Considering strengthening effect of the nanoscale u phase to the b matrix, a strength equation for small-scale crystal is proposed [49,50],
Fig. 9. Schematic diagram of the shearing model between dislocations and the u phase (a) the u phase dispersive in the b matrix. (b) u1 free channels resulted in dislocation slip localized.
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1 2
pffiffiffi
s ¼ s0 þ mb r þ
amb
L ln þ Dsu L b
(1)
where the first term corresponds to friction stress, s0 is 802 MPa for b phase obtained from the experimental results of Song et al. [51]. The second term is due to back-stresses from dislocationedislocation interactions, m is the shear modulus, b is the Burgers vector, r is the dislocation density, the third term originates from the single-arm sources (SAS) strength, where a is a constant prefactor corresponding to the character of the dislocation line and L is the dislocation source length, and the last term Dsu originates from the u phase strengthening effect. Therefore, the yield stress of micropillar mainly depends on the sum of frictional stress, back-stress, and the interaction stress of the dislocations and the u phase, rather than SAS strength. As a result, the proportion of the SAS contribution to the yield stress of micropillar is decreased. Since the u phase is passed by the three partials dislocations, we simply use the cut mechanism to estimate the increased stress by the u phase [36]. Based on the previous work in our group, the normal stress Dsu is about 110 MPa [38]. Calculated from the pffiffiffi equation, the sum of s0 ; 12 mb r; Dsu is 928 MPa. The SAS strength is dependent on the pillar sizes, i.e, the SAS strength of 1 mm pillar is 95 MPa, so the calculated yield strength of 1 mm pillar is 1023 MPa, which is consistent with the experimental value 1001 MPa as shown in Fig. 2(b). 4.3. The interaction between the dislocation and a/b interface In the aged (at 650 C) Ti-55531 alloy micropillars, the exponent of power law, m, is 0.06 (Fig. 2(d)), which implies a much weaker size effect compared with solution-treated micropillars. It can be attributed to the high density of a phase and a/b interface. Compared with the u phase, the size of a phase is much larger and the a phase has the plastic deformation ability. Due to the nature of b-a transformation, the crystallographic features usually follows the Burgers orientation relationship (BOR): {110}b//{0001}a, < 111>b//<1120>a) [26,52,53]. In theory, a maximum of 12 crystallographic orientation a variants can be formed due to the cubic symmetry of the b phase and the BOR between the two phases [53]. But variant selection takes place during transformation, and only a few of the possible 12 a variants are present in a single b crystal [26,54].
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Fig. 10 illustrates the dislocation movement between a phase and b matrix. Variant selection is occurred in the b matrix, as illustrated in the Fig. 10(a). When the applied stress reaches the yield stress, dislocation slip occurs in some a phase with lower Schmid factor. With the load increasing, the dislocations multiply and entangle, as exhibited in Fig. 10(b). The TEM results show that dislocations or slip traces can be observed in some a phase, and the boundaries of those a phase are zigzag. However, the morphologies of other a phases still keep their integrity, which indicates that these a phases do not deform in the compressive process. Increasing the loading stress, more and more a phase deform and lead to working hardening itself, as exhibited in Fig. 10(c) and (d). Consequently, the strength of the whole pillar is enhanced. So the deformation order of a variants has a close relationship with their different crystal orientations. Since the high density of a phase has a random distribution and the dislocation slip in b matrix is truncated by the a phase, the location of the deformation areas is discrete. The dislocation slip is not continuous, and the mean free path of dislocation is shorter than the pillar size. As a result, a much weaker size effect is displayed. On the other hand, the dislocations could be stored in the space between the neighbour a phase or a phase itself. High density of the dislocation can be stored in some a phase, which implies that the strain hardening occurs and the deformation can be locked in local area, as indicated in Fig. 10(d). This result is corresponding with the SHR of the aged micropillars, which is much higher than that of the solution-treated micropillars, as shown in Fig. 3. Since the a phase and the b matrix maintain the BOR {110}b//{0001}a and <111>b//<1120>a, it indicates that some slip systems are well-aligned and slip can transfer through the interfaces and cause slip to transfer from one phase to another. The a phase and the b matrix have the comparatively individual deformation. The high density of a/b interface impedes the continuous movement of dislocation, and the high density of deformable a phase supplies the space of dislocation storage. The coupling effect between the deformable a phase and the high-density a/b interface makes the aged micropillars exhibit excellent plastic deformation and high strength. Our previous works [55] have revealed that the interface between the a phase and the b matrix was semi-coherent and deformable rather than hard barriers without slip. This harmony slip mode is similar to “slip relay” behaviour, following the sequence “slip, dislocation pile-up, stress concentration, slip at higher stress”. As a result, a continuous increase of flow stress is displayed. The main cause for the slip mode is the ductile a and b
Fig. 10. Schematic diagram of the deformation model between dislocations and the a variants with different orientations. (a) Variant selection in the b matrix (b) Dislocations firstly activated in the a phase with highest Schmid factor. (c) Then Dislocations activated in a phase with the second high Schmid factor. (d) Working hardening occurred in the a phase. (e) Individual deformation in the a phase with different orientations.
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phases, both of which possess enough slip systems that are activated at critical stress. The a phase simultaneously play roles of barriers and sink for dislocations. Working hardening, thus, takes place in the a phase. As illustrated in the Fig. 10(d), the deformable a phase with different orientations make great contribution to accommodate the plastic deformation between the two phases. The improved strength (from high density of a/b interface) and plasticity (from working hardening by dislocation-dislocation interaction) can be simultaneously achieved. The synergic deformation of the two phases leads to a highly beneficial strainestress response.
5. Conclusion
4.4. The strengthening by the high density of a phase It well known that a phase plays an important role in strengthening b-titanium alloys. {1010} prismatic slip, {0001} basal slip and {1011} and {1022} pyramidal slips are frequent slip systems in the a phase [53,56]. Since the strength of a phase is dependent on its size, which also exhibits the size effect [27], the yield strength of a phase can be calculated with the following power equation (2):
sa ¼ ka*dn1
(2)
where the power exponent n1 is 0.44 [27] and the constant ka is 620 [57]. As observed in the SEM and TEM results, the average width of a phase is about 100 nm. The yield strength of a phase (sa) is calculated to be approximately 1.2 GPa, lower than the yield strength (1.55 GPa) of aged micropillars. So the a phase is deformable. The strength of micropillars is attributed to the interaction between dislocations and a phase. Based on the Taylor model, the flow stress is described as following [58e60]:
t ¼ t0þCm(br/l)1/2
(3)
where C is a constant, m is the shear modulus, b is the Burgers vector, r is the radius of second particles, and l is the dislocation slip distance [59,60]. The m, b and C can be replaced by a coefficient k. (l/r) is defined as L, which is dependent on the size of a phase. Equation (4) can be simplified as follows:
s ¼ s0þkL1/2
phase is outstanding, which results in the improvement of strain hardening capacity. Moreover, the b matrix will be divided into small region by the a/b interface and the dislocation movement will be limited effectively. The high density of a/b interface enhances trans-interface slip resistance, and hence, increases strength. The results imply that tuning the phase interface structure and distribution by tailoring the size and the density of second phase is an effective method to optimize the strength and plastic deformation of materials.
1. The Ti-55531 alloy pillars with nanoscale u phase show obvious size effect, which means “smaller is stronger”. The strengthening effect of dispersive u phase is limited and the plastic unstability is serious with the pillar size decreasing. However, the yield strength of Ti-55531 alloy pillars with high-density a phase is about 1.5 GPa, which is hardly affected by the pillar sizes. The plastic deformation exhibits great stability which is comparable to the bulk materials. 2. The deformation mechanism of Ti-55531 alloy micropillars with nanoscale u phase is dislocation shearing the u phase, leading to u/b phase transformation. The coherent character of the u/b interface and the dissociation of a perfect 1/2 <111>b dislocation make great contribution to the phase transformation. The u-free channels, which provide an easy slip path for the subsequent dislocations slip are formed. Consequently, the obvious plastic unstability is observed in the strain-stress curves. 3. The excellent plastic stability and high SHR of the Ti-55531 alloy pillars with sub-microscale a phase are attributed to the interaction between the dislocations and the high-density a/b interface. Working hardening in the a phase enhances the yield strength of the whole micropillar. The a phase with different orientations deformed in order ensure the discreteness of dislocation slip activation and dislocation movement, which makes great contribution to the plastic stability. The a/b interface coordinatively and continuously restricts the dislocation movement. Tailoring the size and the density of second phase to tune the phase interface structure and distribution provide a novelty design concept for the high performance materials.
(4)
in our previous work [55], the critical flow stress of matrix, s0, is 0.9 GPa, the constant k is 1.01. So the strength of the aged Ti55531 micropillars s is calculated to be 1.5 GPa, which is consistent with the experimental result 1.55 GPa. 4.5. The comparison of the deformation mechanisms between different structures of phase interfaces
Author contributions section L.X. and Q.S. designed and supervised the project. W.K. performed the experiments data analysis, and write paper. J.S. provided valuable comments and suggestions for the work. All authors contributed to discussions of the results. Declaration of competing interest
The deformation model of the aged micropillars with high density of a phase is different from that of the solution-treated micropillars with nanoscale u phase. The different mechanical behaviours due to the different deformation mechanisms in the solution treated samples and the aged samples. The dislocation slip in the solution-treated micropillars are sensitive to the phase transformation. Once the dislocation shear the u phase, the u-free channels would be formed. The channels against further dislocation slip are obviously affected, which results in deformation localized, low SHR and strain bursts occurred. However, there are no channels formed in the aged micropillars containing the high density of a/b interface. The a phase has the ability of plastic deformation, and the dislocations can be activated inside. The mechanical behaviour exhibits stable plasticity without strain bursts. The ability of storing the dislocations in the high-density a
The authors declare no conflicts of interest. Acknowledgements The authors gratefully thank support from the National Natural Science Foundation of China (51671158, 51621063, 51471129), 973 Program of China (2014CB644003), and the 111 Project 2.0 (PB2018008), Wenjuan Kou would like to acknowledge the help form Shengwu Guo on TEM. Access to the nanoindenter and FIB equipment in CAMP-Nano is also acknowledged. References [1] R.O. Ritchie, The conflicts between strength and toughness, Nat. Mater. 10
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Coupling effect of second phase and phase interface on deformation behaviours in microscale Ti-55531 pillars Wenjuan Kou, Qiaoyan Sun*, Lin Xiao**, Jun Sun State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 7 August 2019 Received in revised form 9 December 2019 Accepted 16 December 2019 Available online xxx
The metastable-b Ti-55531 alloys with different second phases were chosen to investigate coupling effect of second phase and interface as well as the dislocation interaction details under uniaxial compression. In Ti-55531 alloy, nanoscale u phase was acquired by solution treatment, which was coherent with the b matrix. The orientation relationship between hexagonal u and bcc b lattice was (0001)u//(111)b and [1120]u//[110]b. Sub-microscale a phase was acquired by ageing process, following the Burgers orientation relationship (BOR), {110}b//{0001}a and <111>b//<1120>a. The characters of mechanical behaviors and deformation microstructures in this alloy have been analyzed by combining the results from uniaxial compression, scanning electron microscopy (SEM), transmission electron microscopy (TEM) and highresolution TEM. Ti-55531 alloy micropillars with deformable a phase show great plastic stability and high strength, which are attributed to the deformable a phase and the interaction between the dislocations and the high-density a/b interface. However, Ti-55531 alloy micropillars with nanoscale u phase exhibit size effect and poor plastic stability. The deformation mechanism of the Ti-55531 pillars with u phase is dislocation shearing the u phase, which will cause the u/b phase transformation. The u-free channels result in the collective movement of dislocations, performed as the strain bursts in the stressstrain curves. But the dislocation slip between the a phase and the b matrix follows a harmony slip mode, which is similar to “slip relay” behaviour. The results reveal that tuning the morphology of phase interface and the density of second phase to govern the activation, multiplication and movement of dislocation is an effective method to tailor the strength and plastic deformation of materials. The deformation model between the dislocations and the phase interface has great significance to the design of the high performance materials by optimizing the microstructures. © 2019 Elsevier B.V. All rights reserved.
Keywords: Ti alloy Phase interface Microstructure Mechanical properties Microscale
1. Introduction Metals have been the most important materials for human beings in thousands of years. Finding the balance between strength and plasticity is the most effective way to maximize the mechanical properties of material [1]. The traditional strengthening methods were work hardening, solid-solution strengthening, interface strengthening, precipitation hardening and so on [2,3]. The interfaces play important roles in crystalline plasticity as they often serve as obstacles for dislocation motion, as well as dislocation
* Corresponding author. State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, PR China. ** Corresponding author. State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, PR China. E-mail addresses: [email protected] (Q. Sun), [email protected] (L. Xiao). https://doi.org/10.1016/j.jallcom.2019.153421 0925-8388/© 2019 Elsevier B.V. All rights reserved.
sources/sinks [4]. For example, nanocrystalline materials are structurally characterized by a large volume fraction of grain boundaries, which may significantly increase the strength in comparison with conventional coarse-grained polycrystalline materials, but the plastic deformation will be limited by the decreasing of grain size [4,5]. Compared to the classical grain boundaries, introducing the phase interface is another efficient method to enhance the mechanical properties of alloy, because a uniform distribution of the second phase impede dislocation motion which strengthens the alloy directly [2,3]. Usually, the second phases are nanometer scale, and the corresponding strengthening mechanisms can be divided into two categories, the dislocation shearing mechanism and the Orowan dislocation bypassing mechanism, depending on the interaction between moving dislocations and second phases [6,7]. Most of high-performance metallic materials, including Al alloys, Mg alloys, stainless steels, and Ni superalloys, all contain a uniform
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microstructure of the diverse second-phase particles distributed in matrix [8e13]. Magnesium alloys have shown that nano/micro– precipitates can act as sites and paths for void nucleation, crack initiation and subsequent crack propagation during spall failure [14]. The coherent precipitation of cuboidal L12-g’ particles in Nibased superalloys are responsible for the necessary strength at much higher temperatures near to the melting point [15,16]. In addition, the enhancement effect increases with the increase of the second phase content. However, when the content increases to a much higher value, it becomes difficult to start the internal dislocation of the material due to lattice distortion, stress field and other effects [17]. The dislocations are locked at the phase interface and could not be activated and move. The poor strain hardening rate (SHR) of the alloy containing second phase has proved that the locked dislocations at the interface are associated with plastic localization [18,19]. So the nanoscale second phase strengthening has an upper bound. As we known, the strength of crystalline materials is principally determined by the limit to elastic deformation, with subsequent plastic deformation occurring by the nucleation and propagation of dislocations [20]. The interfaces are not only the barriers to dislocation, but also the sources or storage sites for dislocation. For example, A. Misra [21] found that the slip was transferred from gþg0 phase to the b phase via a gþg’ phase dislocation gliding into the semi-coherent interface and converted into a glissile dislocation in the b phase. K.S. Ng [22] found that coating aluminum micro-columns with tungsten could eliminate the strain bursts and significantly increased the strain-hardening rate, because the interface of coating trapped dislocations inside the crystals, thus raising the stored dislocation density by up to three orders of magnitude. So the interfaces not only trap the mobile dislocations but also exist as the sources of dislocation nucleation. If the space between the interfaces is large enough, dislocation movement may transmit cross the interface and dislocation can store and propagate in the space, which ensures the good plastic deformation capability. At the same time, keeping the large volume fraction of interfaces would guarantee the excellent strength of alloys. The metastable b titanium alloys, as the next-generation highperformance materials, their mechanical properties are strongly dependent on the microstructural characteristics [23e26], therefore the second phase in b matrix has been a topic of intensive studies. Tuning the second phase may have a great chance to get a good match between the strength and plasticity. In this study, highdensity a/b interface and discrete nanoscale u/b phase interface were acquired by different heat treatments to investigate the optimizing of strengthening and plasticity by different interface structures. It is worth noticing that the properties of the metastable b-Ti alloys are almost tested from the polycrystalline bulk materials, and the effect of grain boundaries cannot be excluded [27]. Precise mechanistic analysis using nanoindenter becomes widely used to investigate the local area deformation characters [28,29]. It is thought that small-scale experiments on a localized, confined area are required to understand of the fundamental mechanisms on the level of the individual microstructural constituents. Therefore, the micropillar compression technique was adopted to isolating individual microstructural units and selecting particular slip systems for investigation, which is difficult to achieve by compression of bulk samples. In this work, local deformation mechanisms in twophase Ti alloys were investigated by the micropillar compression focusing on coupling effect of second phase and phase interface change local slip behaviour as well as work hardening in compression. This work provides the basis for further understanding of fundamentals on nanomechanics of alloy pillars with specific second phase.
2. Experimental procedures A commercial metastable b-Ti alloy, Tie5Ale5Moe5Ve3Cre1Zr (Ti-55531) bulk was chosen in this work. Two Ti-55531 alloy bulks with 6 mm in diameter and 4 mm in height, were cut using spark machine from the hot rolled bar, and then solution-treated at 950 C for 24 h in vacuum followed by quenching to room temperature in water. The metastable b phase was retained by quenching above the b transus temperature. The achieved b grain size was in the range of 0.5e1 mm. The grain size was measured by Nano Measurer software. One of the bulks needed a further isothermal vacuum annealing, performed at 300 C for 20 h to form a large number of isothermal u phase, which can become nucleus of the stable a phase nucleation [30e32]. Then the annealing temperature was further increased to 650 C for 15 h to dissolute the remained u phase and promote the growth of a phase by clustering different a variants into self-accommodating morphologies [31]. Therefore, one b Ti-55531 alloy bulk with nanoscale u phase and the other one with high density of sub-microscale a phase were produced. The square bulk was mechanically and electrochemically polished before fabricating into micropillars. The grain orientation was determined via electron backscattered diffraction (EBSD). For both of the Ti-55531 alloy bulks, grains oriented to <101>b were selected to fabricate micropillars using Focus Ion Beam (FIB) technique, as shown in Fig. 1(a) and (b). The SEM microstructure of the aged (at 650 C) Ti-55531 alloy was shown in Fig. 1(c), which exhibited high-density a/b interface. A group of single-crystal micropillars were fabricated using the FEI Helios operated at an ion beam voltage of 30 kV with a variety of currents, as shown in Fig. 1(d). The micropillar diameter, ranges from 150 nm to 2.5 mm, with an aspect ratio of ~2.5. The taper of the micropillars is between 6 and 2 . Three to five samples were prepared each size. Uniaxial compression experiments were conducted in Hysitron Ti-950 nanoindenter with a 10 mm flat punch diamond tip at a constant nominal strain rate of 1 103/s. The loading mode was displacement control. The loading-displacement dates would be acquired after compression. The post-compression morphology of the micropillars was observed with SEM. All TEM specimens were prepared by lifting out technique using a nanomanipulator (AutoProbe 200, Omniprobe, Inc.) and transferring them onto Cu grids. The micropillar samples were then thinned to the electron-transparent thickness (～100 nm) by using the FIB. 3. Results 3.1. Mechanical behavior of uniaxial compression Typical stressestrain curves of the solution-treated and the aged (at 650 C) Ti-55531 alloy micropillars with various diameters compressed along <101>b orientation are shown in Fig. 2(a) and (c). The yield strength is defined as the flow stress of the micropillar at 0.2% engineering strain. For the solution-treated Ti-55531 alloy micropillars, the strain bursts are more and more obvious with the decrease of diameter, as shown in Fig. 2(a). The relevant yield strength increases from 0.9 GPa to 1.5 GPa, showing the “smaller is stronger” phenomenon, as shown in Fig. 2(b). The power-law fitting gives a relationship between the yield strength and diameter, s~Dm , the exponent m is 0.335. For the aged Ti-55531 alloy micropillars, the stressestrain curves are smooth and continuous, as shown in Fig. 2(c). The yield strength is about 1.5 GPa, regardless of the pillar sizes, as shown in Fig. 2(d). The exponent m is 0.06. The results indicate that the size effect of the aged micropillars is much weaker than that of the solution-treated micropillars. On a close examination, the stress-strain curves of the aged micropillars show a smooth and stable plastic deformation behavior, which is much
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Fig. 1. (a) EBSD map of the solution-treated Ti-55531 alloy bulk specimen before FIB milling (the white lines indicate location marks), (b) EBSD map of the aged (at 650 C) Ti-55531 alloy bulk specimen before FIB milling, (c) Typical SEM microstructure of the aged (at 650 C) Ti-55531 alloy, (d) Typical SEM morphology of the micropillar.
Fig. 2. Compressive behaviors of the Ti55531 micropillars (a) The engineering stressestrain curves and (b) yield strengths (at 0.2% plastic strain) versus pillar diameter of the solution-treated Ti-55531 alloy micropillars, (c) The engineering stressestrain curves and (d) yield strengths (at 0.2% plastic strain) versus pillar diameter of the aged Ti-55531 alloy micropillars.
similar with the bulk sample [33]. So the aged Ti-55531 micropillars exhibit an excellent combination of high strength and stable plasticity. The strain hardening rate (SHR) is quantified in Fig. 3 as a function of pillar diameter. Due to the displacement bursts during the stressestrain response of the micropillars, SHR is defined as the
slope between the true stressestrain data values at 3% and 10% strain. This definition is similar to that used in an analogous study [34,35]. The SHR of the aged micropillars is higher than that of the solution-treated micropillars. An increase in SHR of the solutiontreated micropillars is observed to correlate with decreasing diameter. However, the SHR of the aged micropillars slightly
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observed on the surfaces instead of the significant slip steps in solution-treated micropillars, as indicated by the red arrows in Fig. 4(e) and (f). At the same time, many fine slip steps are visible on the sides of micropillars. Based on the analysis of slip traces, {112}b <111>b slip system is activated in the aged Ti-55531 alloy micropillars. 3.3. Deformation mechanisms of the solution-treated and aged (at 650 C) Ti-55531 alloy micropillars
Fig. 3. The SHR for the solution-treated (red points) and the aged (black points) Ti55531 alloy micropillars with different diameters. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
increases with the diameter. 3.2. Deformation modes of solution-treated and aged (at 650 C) Ti55531 alloy micropillars Fig. 4(a)e(c) show SEM images of the deformed solution-treated and aged Ti-55531 alloy micropillars, respectively. A group of parallel slip bands and several large slip steps are observed on the surface of the solution-treated Ti-55531 alloy micropillar, as indicated by the white dash lines in Fig. 4(a)e(c). On a close examination, only one slip system is activated in the solution-treated micropillars. The angle between the slip plane and the top surface of pillar ({101}b) is 53 , which indicates that the {112}b <111>b slip system is activated in the solution-treated micropillars, as shown in Fig. 4(c). The same slip system is observed in other b titanium alloys [36e38]. For the aged Ti-55531 alloy micropillars, tortuous slip traces are
3.3.1. Microstructure of the micropillars before deformation Fig. 5(a) shows typical TEM microstructure of the solutiontreated Ti-55531 alloy micropillar before deformation. The selected area electron diffraction (SAED) pattern analysis along the <011>b zone axis of b matrix shows that the primary components in the solution-treated Ti-55531 alloy includes the b matrix and the u phase. Nanoscale u phase homogeneously distributes in the b matrix. These u phase are produced through athermal transformation from the b to the u during water quenching. The size of u phase is only several nanometers. Fig. 5(b)-(d) shows typical TEM microstructure of the aged Ti55531 alloy micropillar before deformation. High density of a phase is acquired in the b matrix. The size of a phase is 100e300 nm, which is much larger than that of u phase. The b matrix has a common b-{110} pole with the a-{0001} pole. The a phase and the b matrix own the following Burgers orientation relationship: {110}b//{0001}a and <111>b//<1120>a [39e41]. The a phase is short rod-like and uniformly distributes in the b matrix, as shown in Fig. 5(b)-(c). Fig. 5(d) shows that the boundaries of a phase are clear and smooth. The volume fraction of a phase is about 40%, obtained from the SEM images by the Photoshop software. The size of a/b interface was much larger. 3.3.2. Microstructure in the deformed micropillars Fig. 6 shows the TEM micrograph of the ~20% deformed solution-treated Ti-55531 alloy micropillar. The slip traces in the TEM image confirm that the {112}b <111>b slip system is activated, as shown in Fig. 6(a). A set of parallel slip lines are observed inside
Fig. 4. SEM morphology of the deformed micropillars with different diameters (a)-(c) the deformed solution-treated Ti-55531 alloy micropillars, (d)-(f) the deformed aged Ti-55531 alloy micropillars.
W. Kou et al. / Journal of Alloys and Compounds 820 (2020) 153421
Fig. 5. Microstructures of the micropillars before deformation. (a) the distribution of the u phase in the b matrix, (b) the distribution of a phase in the b matrix, (c) the bright-field image and (d) the dark-field image of a phase.
5
amount of u2 has little change in the same region along slip, as shown in Fig. 6(d)-(e). These observations suggest that a channel depleted of the u1 phase is formed along the slip line. Thus, the absence of u1 inside slip traces indicates a phase transformation from the u1 to the b matrix under compressive stress. The similar results are also observed in some other b-Ti alloys [36,42]. Therefore, the deformation mechanisms in the solution-treated Ti-55531 alloy micropillar include dislocation interaction with the u phase and the stress-induced phase transformation along slip planes. Fig. 7 shows the TEM micrographs of the deformed aged (at 650 C) Ti-55531 alloy micropillar. No slip bands can be distinguished and the boundaries of some a phase are blurry and tortuous. It is quite difficult to recognize the interface between the a phase and the b matrix, as shown in the magnified area in Fig. 7(a). The Fig. 7(b)-(c) show the bright-field and dark-field images of the deformed a phase, respectively. The slip traces can be found in some a phase and even some slip steps are observed in the interface between the a phase and the b matrix, as indicated by the red narrows in Fig. 7(c)-(d). Some parallel dislocations are stored in the a phase (Fig. 7(e)), which will introduce working hardening. Fig. 8(a) shows the high-resolution transmission electron microscope (HRTEM) image of the a/b interface. There are no obvious dislocations pile up near the a/b interface, and the dislocations can be observed in the a phase, as shown in Fig. 8(b). This result indicates that the a phase and the b matrix undertake the plasticity simultaneously. 4. Discussion
the micropillar, as indicated by the white dash arrows in Fig. 6(b). Further observation of Fig. 6(c) shows a bright-field image of one slip trace and the inset of in Fig. 6(c) is the corresponding diffraction pattern, which shows weak diffraction intensity of the u1, and a normal diffraction intensity of the u2, as marked by the two white circles. The related dark-field TEM images using the u1 and the u2 reflections show that two u variants have the same amount and uniformly disperse throughout the b matrix in the non-slip region, but the u1 precipitates almost disappear along slip traces and the
4.1. The interaction between the dislocation and u/b interface The yield strength of the solution-treated Ti-55531 alloy single crystal micropillar increases with the decrease of pillar diameter in a power law of s fDm . The strengthening exponent, m, is 0.335. It’s well known that when the pillars are composed of the secondary particles and the matrix, interactions between the dislocations and secondary particles weaken the size effect [27,43e45]. In this work, it can be attributed to the formation of nanoscale u
Fig. 6. Microstructures in the deformed solution-treated Ti-55531 alloy micropillar. (a) the whole morphology of the deformed micropillar, (b) slip traces in the pillar, (c) the brightfield image of the slip line, the related dark-field TEM images of (d) the u1 and (e) the u2.
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Fig. 7. TEM microstructures in the deformed aged (at 650 C) Ti-55531 alloy micropillar. (a) the deformed a phase in the b matrix, (b) the bright-field image and (c) the dark-field image of the a phase, (d) slip step in the a phase, (e) dislocations stored in the a phase.
Fig. 8. (a)HRTEM images of the deformed a/b interface, (b) Inverse Fourier transform of Fig. 8(a).
phase. An interface and u phase are introduced into pillars to modify the size effect on strength. As mentioned above, the deformation-induced microstructure evolution reveals that the phase transformation from the u1 to the b matrix occurred under uniaxial compression. The orientation relationship between hexagonal u and body-centered cubic (bcc) b lattice is (0001)u//(111)b and [1120]u//[110]b [46]. It reveals that the prismatic slip plane {1100}u of the u phase is parallel to the {112}b slip plane of the b matrix. Based on the slip trace analysis, {112}b<111>b slip system is activated in the b matrix. Taking into account the relatively low misfit between the lattices and the coherent character of the u/b interface [47], such a coherence of the slip planes in b and u facilitates the slip transfer from the {112}b planes onto the {1100}u planes. The dissociation of dislocation lead to the stress-induced phase transformation. The motion of a perfect 1/2 <111>b dislocation on the {112}b slip plane is blocked by the u phase and dissociates into three partials, b1 ¼ 1/12 <111>b, b2 ¼ 1/3 <111>b and b3 ¼ 1/12 <111>b, on three consecutive {112} b planes [36]. The movement of these dislocation partials causes the u phase back into the b phase. The phase transformation phenomenon follows the traditional deformation mechanism, dislocation
shearing the second phase. Among the four possible u variants, only one variant’s [0001]u direction parallel to a particular [111]b direction [41,48]. Therefore, only one u variant can transform back to the b matrix. And the other three u variants remain unchanged under the same stress condition. The dislocations-u interaction suggests that the dislocations shear the u phase along the {112}b//{1100}u slip planes, forming channels that are devoid of the u1 phase, as indicated in Fig. 9(b). The channels cause that the resistance against further dislocation movement reduced, so the dislocation slip are localized. The dislocation motion along slip planes results in the formation of dislocation channels and the plastic flow localization, which would introduce the strain bursts. The SHR of the solution-treated micropillars verifies that the model of dislocation motion is dislocation slip localized without multiplication or accumulation so that the usual mean-field conditions for forest hardening are destroyed [20,34].
4.2. The strengthening by the nanoscale u phase Considering strengthening effect of the nanoscale u phase to the b matrix, a strength equation for small-scale crystal is proposed [49,50],
Fig. 9. Schematic diagram of the shearing model between dislocations and the u phase (a) the u phase dispersive in the b matrix. (b) u1 free channels resulted in dislocation slip localized.
W. Kou et al. / Journal of Alloys and Compounds 820 (2020) 153421
1 2
pffiffiffi
s ¼ s0 þ mb r þ
amb
L ln þ Dsu L b
(1)
where the first term corresponds to friction stress, s0 is 802 MPa for b phase obtained from the experimental results of Song et al. [51]. The second term is due to back-stresses from dislocationedislocation interactions, m is the shear modulus, b is the Burgers vector, r is the dislocation density, the third term originates from the single-arm sources (SAS) strength, where a is a constant prefactor corresponding to the character of the dislocation line and L is the dislocation source length, and the last term Dsu originates from the u phase strengthening effect. Therefore, the yield stress of micropillar mainly depends on the sum of frictional stress, back-stress, and the interaction stress of the dislocations and the u phase, rather than SAS strength. As a result, the proportion of the SAS contribution to the yield stress of micropillar is decreased. Since the u phase is passed by the three partials dislocations, we simply use the cut mechanism to estimate the increased stress by the u phase [36]. Based on the previous work in our group, the normal stress Dsu is about 110 MPa [38]. Calculated from the pffiffiffi equation, the sum of s0 ; 12 mb r; Dsu is 928 MPa. The SAS strength is dependent on the pillar sizes, i.e, the SAS strength of 1 mm pillar is 95 MPa, so the calculated yield strength of 1 mm pillar is 1023 MPa, which is consistent with the experimental value 1001 MPa as shown in Fig. 2(b). 4.3. The interaction between the dislocation and a/b interface In the aged (at 650 C) Ti-55531 alloy micropillars, the exponent of power law, m, is 0.06 (Fig. 2(d)), which implies a much weaker size effect compared with solution-treated micropillars. It can be attributed to the high density of a phase and a/b interface. Compared with the u phase, the size of a phase is much larger and the a phase has the plastic deformation ability. Due to the nature of b-a transformation, the crystallographic features usually follows the Burgers orientation relationship (BOR): {110}b//{0001}a, < 111>b//<1120>a) [26,52,53]. In theory, a maximum of 12 crystallographic orientation a variants can be formed due to the cubic symmetry of the b phase and the BOR between the two phases [53]. But variant selection takes place during transformation, and only a few of the possible 12 a variants are present in a single b crystal [26,54].
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Fig. 10 illustrates the dislocation movement between a phase and b matrix. Variant selection is occurred in the b matrix, as illustrated in the Fig. 10(a). When the applied stress reaches the yield stress, dislocation slip occurs in some a phase with lower Schmid factor. With the load increasing, the dislocations multiply and entangle, as exhibited in Fig. 10(b). The TEM results show that dislocations or slip traces can be observed in some a phase, and the boundaries of those a phase are zigzag. However, the morphologies of other a phases still keep their integrity, which indicates that these a phases do not deform in the compressive process. Increasing the loading stress, more and more a phase deform and lead to working hardening itself, as exhibited in Fig. 10(c) and (d). Consequently, the strength of the whole pillar is enhanced. So the deformation order of a variants has a close relationship with their different crystal orientations. Since the high density of a phase has a random distribution and the dislocation slip in b matrix is truncated by the a phase, the location of the deformation areas is discrete. The dislocation slip is not continuous, and the mean free path of dislocation is shorter than the pillar size. As a result, a much weaker size effect is displayed. On the other hand, the dislocations could be stored in the space between the neighbour a phase or a phase itself. High density of the dislocation can be stored in some a phase, which implies that the strain hardening occurs and the deformation can be locked in local area, as indicated in Fig. 10(d). This result is corresponding with the SHR of the aged micropillars, which is much higher than that of the solution-treated micropillars, as shown in Fig. 3. Since the a phase and the b matrix maintain the BOR {110}b//{0001}a and <111>b//<1120>a, it indicates that some slip systems are well-aligned and slip can transfer through the interfaces and cause slip to transfer from one phase to another. The a phase and the b matrix have the comparatively individual deformation. The high density of a/b interface impedes the continuous movement of dislocation, and the high density of deformable a phase supplies the space of dislocation storage. The coupling effect between the deformable a phase and the high-density a/b interface makes the aged micropillars exhibit excellent plastic deformation and high strength. Our previous works [55] have revealed that the interface between the a phase and the b matrix was semi-coherent and deformable rather than hard barriers without slip. This harmony slip mode is similar to “slip relay” behaviour, following the sequence “slip, dislocation pile-up, stress concentration, slip at higher stress”. As a result, a continuous increase of flow stress is displayed. The main cause for the slip mode is the ductile a and b
Fig. 10. Schematic diagram of the deformation model between dislocations and the a variants with different orientations. (a) Variant selection in the b matrix (b) Dislocations firstly activated in the a phase with highest Schmid factor. (c) Then Dislocations activated in a phase with the second high Schmid factor. (d) Working hardening occurred in the a phase. (e) Individual deformation in the a phase with different orientations.
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phases, both of which possess enough slip systems that are activated at critical stress. The a phase simultaneously play roles of barriers and sink for dislocations. Working hardening, thus, takes place in the a phase. As illustrated in the Fig. 10(d), the deformable a phase with different orientations make great contribution to accommodate the plastic deformation between the two phases. The improved strength (from high density of a/b interface) and plasticity (from working hardening by dislocation-dislocation interaction) can be simultaneously achieved. The synergic deformation of the two phases leads to a highly beneficial strainestress response.
5. Conclusion
4.4. The strengthening by the high density of a phase It well known that a phase plays an important role in strengthening b-titanium alloys. {1010} prismatic slip, {0001} basal slip and {1011} and {1022} pyramidal slips are frequent slip systems in the a phase [53,56]. Since the strength of a phase is dependent on its size, which also exhibits the size effect [27], the yield strength of a phase can be calculated with the following power equation (2):
sa ¼ ka*dn1
(2)
where the power exponent n1 is 0.44 [27] and the constant ka is 620 [57]. As observed in the SEM and TEM results, the average width of a phase is about 100 nm. The yield strength of a phase (sa) is calculated to be approximately 1.2 GPa, lower than the yield strength (1.55 GPa) of aged micropillars. So the a phase is deformable. The strength of micropillars is attributed to the interaction between dislocations and a phase. Based on the Taylor model, the flow stress is described as following [58e60]:
t ¼ t0þCm(br/l)1/2
(3)
where C is a constant, m is the shear modulus, b is the Burgers vector, r is the radius of second particles, and l is the dislocation slip distance [59,60]. The m, b and C can be replaced by a coefficient k. (l/r) is defined as L, which is dependent on the size of a phase. Equation (4) can be simplified as follows:
s ¼ s0þkL1/2
phase is outstanding, which results in the improvement of strain hardening capacity. Moreover, the b matrix will be divided into small region by the a/b interface and the dislocation movement will be limited effectively. The high density of a/b interface enhances trans-interface slip resistance, and hence, increases strength. The results imply that tuning the phase interface structure and distribution by tailoring the size and the density of second phase is an effective method to optimize the strength and plastic deformation of materials.
1. The Ti-55531 alloy pillars with nanoscale u phase show obvious size effect, which means “smaller is stronger”. The strengthening effect of dispersive u phase is limited and the plastic unstability is serious with the pillar size decreasing. However, the yield strength of Ti-55531 alloy pillars with high-density a phase is about 1.5 GPa, which is hardly affected by the pillar sizes. The plastic deformation exhibits great stability which is comparable to the bulk materials. 2. The deformation mechanism of Ti-55531 alloy micropillars with nanoscale u phase is dislocation shearing the u phase, leading to u/b phase transformation. The coherent character of the u/b interface and the dissociation of a perfect 1/2 <111>b dislocation make great contribution to the phase transformation. The u-free channels, which provide an easy slip path for the subsequent dislocations slip are formed. Consequently, the obvious plastic unstability is observed in the strain-stress curves. 3. The excellent plastic stability and high SHR of the Ti-55531 alloy pillars with sub-microscale a phase are attributed to the interaction between the dislocations and the high-density a/b interface. Working hardening in the a phase enhances the yield strength of the whole micropillar. The a phase with different orientations deformed in order ensure the discreteness of dislocation slip activation and dislocation movement, which makes great contribution to the plastic stability. The a/b interface coordinatively and continuously restricts the dislocation movement. Tailoring the size and the density of second phase to tune the phase interface structure and distribution provide a novelty design concept for the high performance materials.
(4)
in our previous work [55], the critical flow stress of matrix, s0, is 0.9 GPa, the constant k is 1.01. So the strength of the aged Ti55531 micropillars s is calculated to be 1.5 GPa, which is consistent with the experimental result 1.55 GPa. 4.5. The comparison of the deformation mechanisms between different structures of phase interfaces
Author contributions section L.X. and Q.S. designed and supervised the project. W.K. performed the experiments data analysis, and write paper. J.S. provided valuable comments and suggestions for the work. All authors contributed to discussions of the results. Declaration of competing interest
The deformation model of the aged micropillars with high density of a phase is different from that of the solution-treated micropillars with nanoscale u phase. The different mechanical behaviours due to the different deformation mechanisms in the solution treated samples and the aged samples. The dislocation slip in the solution-treated micropillars are sensitive to the phase transformation. Once the dislocation shear the u phase, the u-free channels would be formed. The channels against further dislocation slip are obviously affected, which results in deformation localized, low SHR and strain bursts occurred. However, there are no channels formed in the aged micropillars containing the high density of a/b interface. The a phase has the ability of plastic deformation, and the dislocations can be activated inside. The mechanical behaviour exhibits stable plasticity without strain bursts. The ability of storing the dislocations in the high-density a
The authors declare no conflicts of interest. Acknowledgements The authors gratefully thank support from the National Natural Science Foundation of China (51671158, 51621063, 51471129), 973 Program of China (2014CB644003), and the 111 Project 2.0 (PB2018008), Wenjuan Kou would like to acknowledge the help form Shengwu Guo on TEM. Access to the nanoindenter and FIB equipment in CAMP-Nano is also acknowledged. References [1] R.O. Ritchie, The conflicts between strength and toughness, Nat. Mater. 10
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