High Schmid Factor Research Articles

Crack initiation mechanism of a silicide-containing high-strength Ti–5Al-7.5V alloy under low-cycle fatigue loading

In this work, the dual phase titanium alloy Ti–5Al-7.5V was subjected to low-cycle fatigue at room temperature to reveal the deformation mechanisms of fatigue and crack initiation. Transmission electron microscope analysis showed that planar dislocation slip, most of them localized at the basal and prismatic planes of α phase, is the primary deformation mode of low-cycle fatigue. Multiple slips operate concurrently in the high Schmid factor planes within a single grain. Moreover, a limited number of observed microcracks were formed along the basal slip bands. Electron back-scattered diffraction analysis evidenced that numerous microcracks were formed along basal planes. And, the microcracks were confined in primary α grains without propagation to surrounding transformed β matrix, indicating that the alloy exhibits a high tolerance to microcrack propagation. The α grain aggregate oriented for basal slip is a fatigue-critical microstructure configuration, which provides a high Schmid factor path by linking adjacent grains and potentially lead to internal crack initiation with the formation of a field of facets in the cycling process. While the silicides were observed in contact with the microcracks and slip bands, no evidence of crack initiation from silicides was detected. Given that the microcracks were formed along the pre-existing slip bands, it remains an open question whether the silicides can act as the dislocation sources for planar slips and facilitate crack nucleation from these silicides.

Resolving intragranular stress fields in plastically deformed titanium using point-focused high-energy diffraction microscopy

The response of a polycrystalline material to a mechanical load depends not only on the response of each individual grain, but also on the interaction with its neighbors. These interactions lead to local, intragranular stress concentrations that often dictate the initiation of plastic deformation and consequently the macroscopic stress–strain behavior. However, very few experimental studies have quantified intragranular stresses across bulk, three-dimensional volumes. In this work, a synchrotron X-ray diffraction technique called point-focused high-energy diffraction microscopy (pf-HEDM) is used to characterize intragranular deformation across a bulk, plastically deformed, polycrystalline titanium specimen. The results reveal the heterogenous stress distributions within individual grains and across grain boundaries, a stress concentration between a low and high Schmid factor grain pair, and a stress gradient near an extension twinning boundary. This work demonstrates the potential for the future use of pf-HEDM for understanding the local deformation associated with networks of grains and informing mesoscale models.Graphical abstract

Analysis of slip transfer behavior of tantalum during quasi in-situ compression

This paper reports a quasi in-situ study on the plastic deformation behavior of high purity tantalum, particularly the slip activation and slip transfer, using the electron backscatter diffraction method. We found that the rotation degree of grains is in the range of 0–15°; the rotation axes of slip-activated grains are mainly concentrated in the three corners, while the axes of slip-transfer ones are concentrated near {111} corner in the stereographic triangle. Microstructural parameters including grain size and grain aspect ratio were found to have no apparent relationships with the slip activation or slip transfer process. Most m' factors for the grains underwent slip-transfer are larger than 0.27, and most slip systems involved in the slip-transfer observations are associated with relatively high Schmid factors (SFs), indicating that slip would more easily transfer through the boundaries with large m' factors. In addition, according to the distribution of geometrical necessary dislocation density and the SF of slipping activated grains, we found the slip transfer process is affected by a combination of factors, including the SF, m' factor, and the strain concentration in local regions.

Heterogeneous fiberous structured Mg-Zn-Zr alloy with superior strength-ductility synergy

• The heterogeneous fiberous structured ZK60 Mg alloy was obtained by conventional extrusion method with high yield strength of ∼ 345 MPa, ultimate tensile strength of ∼ 370 MPa and high tensile strain of ∼ 20.5%, superior than most ZK60 Mg alloys reported so far. • The excellent mechanical properties were mainly attributed to the heterogeneous fiberous structure that was characterized by alternating coarse- and fine-grain layers, nanoscale precipitates and profuse < c + a > dislocations. The novel heterogeneous fiberous structured ZK60 Mg alloy have achieved superior strength-ductility synergy. • A novel design of alternating coarse- and fine-grain layered structure was considered to be a general strategy for promoting the strength-ductility synergy of hexagonal close-packed (hcp) metals. Here we reported a heterogeneous fiberous structured Mg-5.6Zn-0.6Zr (wt%) alloy obtained by conventional extrusion method, which exhibited high yield strength of ∼ 345 MPa, ultimate tensile strength of ∼ 370 MPa, and high tensile strain of ∼ 20.5%, superior to most of the Mg-Zn based alloys reported so far. The extraordinarily high mechanical properties were mainly attributed to the heterogeneous fiberous structure consisting of alternating coarse- and fine-grain layers. Grains in the different layers grew into the neighboring layers, ensuring a good layer bonding. A high Schmid factor and geometric compatibility factor for pyramidal slip led to full slip transfer between the neighboring coarse grains and fine grains, which could help to release the stress concentration and avoid early fracture. The profuse activated <c + a> glide dislocations could render the unprecedented high tensile strain. The constraint by the hard fine-grain domains made the soft coarse-grain domains strong like the hard fine-grain domains, as well as the nanoscale precipitates pinning dislocations, contributed to the high strength. The heterogeneous microstructure design was shown to have synergistic improvement in strength-ductility balance, which could be an inspiring strategy to improve mechanical properties of hexagonal close-packed (hcp) metals.

Tensile properties and slip deformation behavior of pure titanium thin wire with a small diameter-to-grain-size ratio

To investigate the tensile properties and slip deformation behavior of pure titanium thin wires with a small ratio of the diameter to the grain size, tensile tests and a stepwise tensile test were performed using specimens with a diameter of approximately 170 μm and grain sizes of 17 and 87 μm, corresponding to diameter-to-grain-size ratios of 10 and ∼2, respectively. The specimen with a diameter-to-grain-size ratio of 10 fractured through the growth of voids. The fracture morphology was similar to that of the bulk specimens. On the other hand, for specimens with a diameter-to-grain-size ratio of 2, fracture occurs owing to the local deformation, in which primary slip systems are activated in each grain. The stepwise tensile test of the specimen with a diameter-to-grain-size ratio of 2 indicated that the slip deformation tended to occur from the large grains. Moreover, the activities of the slip systems of grains were evaluated using the Schmid factor (SF) and critical resolved shear stress (CRSS) of each slip system. It was noted that slip systems with the highest SF∙CRSS−1 were activated for 30 out of 33 grains.

Multiscale analysis of interior cracking behavior of Ni-based superalloy fabricated by selective laser melting under very-high-cycle-fatigue at high-temperature

The fatigue test at high-temperature of selective laser melting Ni-based superalloy was performed to reveal the mechanism of interior cracking behavior by multiple analysis methods in the very-high-cycle-fatigue regime. Due to the inhibition effect of oxide layer, the interior multi-defects assisted facetted cracking becomes a significant failure mode. Large grain deformation mainly occurs on the fracture surface, and slip systems with high Schmid factor are activated by high-temperature. The precipitates in the matrix hinder the dislocation movement, resulting in dislocation accumulation and stress concentration increase, which makes it easier for microcracks initiation. The initiated microcracks with crack deflection caused by high angle grain boundaries propagate transgranularly to form a nearly circular region and undergo fast unstable growth, eventually leading to fracture. • The microcracks propagate transgranularly along the maximum shear stress plane. • {111}<112> slip system with high Schmid factor is activated by high-temperature. • Interior multi-defects assisted facetted cracking is the predominant failure mode.

Effect of in-lath slip strength on the strain partitioning in a dual-phase steel investigated by high-resolution digital image correlation and crystal plasticity simulations

In this study, the effect of different modeling hypotheses for the plastic deformation of lath martensite was investigated through an integrated experimental–numerical approach. The local plastic strain distribution of a dual-phase steel with a coarse microstructure was quantified by high-resolution digital image correlation analysis. The same area was reproduced in a crystal plasticity finite element model using the electron backscatter diffraction measurement of the specimen surface prior deformation. Different modeling hypotheses in terms of in-lath and out-of-lath slip strength as well as boundary and bulk elements were explored. It was found that early plastic deformation in lath martensite grains predominantly took place at various interfaces in the form of slip bands parallel to the in-lath slip planes in blocks exhibiting high in-lath Schmid factor. A comparison between experiment and simulations suggested that assuming a lower strength and hardening rate for in-lath slip systems of boundary elements better reproduced the plastic strain fields in martensite grains. However, the different models showed limited effect on the strain distribution within ferrite grains and on the local stress–strain path at void nucleation sites. This suggested that the main factor affecting early strain concentration and subsequent damage initiation in ferrite grains was the phase morphology and strength contrast.

Accurate determination of active slip systems for improved geometrical criteria of basal-to-basal slip transfer at grain boundaries in pure Mg

Basal-to-basal slip transfer across grain boundaries was analyzed through the combination of slip trace analysis and electron back-scatterer diffraction in weakly-textured pure Mg specimens deformed in tension. Basal slip was the dominant deformation mechanism in many grains, and slip transfer/blocking was assessed at 103 grain boundaries. In addition, the actual active slip system(s) in 170 grains were determined through the analysis of the grain rotation as a result of plastic slip along the basal slip systems. Finally, the twist angle θ (formed between the traces of both active slip planes in the grain boundary plane) was determined in selected cases by the progressive removal of the material by a focus ion beam to measure the grain boundary orientation within the sample. It was found that the basal slip system with the highest global Schmid factor was the most active one in only 49.3% of the grains. In 25.7% of the grains, the basal slip system with the highest Schmid factor was not active. The analysis of basal-to-basal slip transfer/blocking showed that slip transfer is likely to occur if mαβ′ > 0.73. In the cases in which mαβ′ > 0.73 and slip transfer did not occur, it was found that the twist angle θ > 60°. Moreover, slip transfer is unlikely to take place if the trace of one of the active slip systems across the boundary is parallel to the grain boundary.

Finite strain crystal plasticity-phase field modeling of twin, dislocation, and grain boundary interaction in hexagonal materials

Twin, dislocation, and grain boundary interaction in hexagonal materials, such as Mg, Ti, and Zr, has critical influence on the materials’ mechanical properties. The development of a microstructure-sensitive constitutive model for these deformation mechanisms is the key to the design of high-strength and ductile alloys. In this work, we have developed a mechanical formulation within the finite strain framework for modeling dislocation slip- and deformation twinning-induced plasticity. A dislocation density-based crystal plasticity model was employed to describe the dislocation activities, and the stress and strain distributions. The model was coupled with a multi-phase-field model to predict twin formation and twin-twin interactions. The coupled model was then employed to study twin, dislocation, and grain boundary interactions in Mg single- and polycrystals during monotonic and cyclic deformation. The results show that twin-twin interactions can enhance the strength by impeding twin propagation and growth. The role of dislocation accommodation on twin-twin interactions was twofold. Dislocation slip diminished twin-twin hardening by relieving the development of back-stresses, while it effectively relaxed the stress concentration near twin-twin intersections and thus may alleviate crack nucleation. The plastic anisotropy in each grain and the constraints imposed by the local boundary conditions resulted in stress variations among grains. This stress heterogeneity was responsible for the observed anomalous twinning behaviour. That is, low Schmid factor twins were activated to relax local stresses and accommodate the strain incompatibility, whereas the absence of high Schmid factor twins was associated with slip band-induced stress relaxation.

In vitro corrosion and in vivo behavior of high strength Mg-6Zn-1Mn alloy wire for gastrointestinal anastomosis nail application

Ti and its alloy staples can be retained in the human body for a long period because of their excellent corrosion resistance and thus requires revision surgery for removal. In this study, biodegradable Mg-6Zn-1Mn alloy staples were fabricated using ∼99.8 % area reduction cold drawing, whose service performance was evaluated by in vitro corrosion and in vivo tests. The high strength (∼340 MPa) of staples is mainly attributed to the formation of fine grains, nanoparticles, and additional dislocations. Moreover, owing to the effect of fine grains, as well as the high Schmid factor of prismatic ⟨a⟩ slip and pyramidal ⟨c+a⟩ slip, the staples also exhibit acceptable ductility (∼10 %). The in vitro corrosion results indicate that staple fractures occurred after immersion for 21 h in a single PBS solution. With the addition of ∼0.5 g/L bovine serum albumin (BSA), the time required to maintain the mechanical integrity of staples can expand to 90 h. This is mainly related to the adsorption and chelating effects between BSA and Mg matrix. After the implantation surgery, all rabbits fully recovered with normal oral intake, and Mg ions generated by degradation effectively promoted the absorption of the alimentary system. Therefore, the Mg-6Zn-1Mn alloy staples fabricated in this study exhibit desired effect, and excellent clinical application prospects.

Comprehensive study of hot compression behaviors and microstructure evolution of solutionized 6082 aluminum alloy extruded bar

Recently, an efficient integrated forging process has been proposed in which solutionized aluminum alloy extruded bars are directly hot forged and quenched. In this study, the hot deformation behaviors and microstructure evolution of 6082 aluminum alloy extruded bar was investigated via isothermal compression tests under the temperature range of 400–535 ℃ and strain rates range of 0.1–10 s−1 with different strains. The deformation behaviors were described by the established strain-compensated constitutive model and processing maps. The microstructure evolution of the deformed specimens was revealed by electron back scattered diffraction (EBSD) and transmission electron microscopy (TEM). It was found that the Zener-Hollomon (Z) parameter, which involved temperature and strain rate, exerted a considerable influence on the deformation behaviors and microstructure evolution. Deformation-induced extensive dislocations were pinned by the dispersoids and generated cellular substructures under high ln Z (i.e. low temperature or high strain rate), potentially triggering dynamic instability. The tangled dislocations pinned by the insoluble dispersoids continued to overcome the pinning points as ln Z decreased, while the dislocations were consumed by the rotation of subgrain boundaries. As a result, the geometrically necessary dislocation (GND) was decreased with the significant increase of the fraction of high angle grain boundaries (HAGBs). In addition, the stable-end orientations, namely, Brass {011}< 211 > and Goss {011}< 001 > texture components with high Schmid Factors (SFs) are generated during compression, facilitating the dislocation movement and thus promoting the fraction of recrystallization. The above findings demonstrate the foundation for improving forming performance and optimizing the processing parameters for the integrated forging process.

Microstructure evolution and mechanical properties of the Mg–5Al–1Mn-0.5Zn-xCa alloys prepared by regular extrusion

High strength-ductility synergy Mg–5Al–1Mn-0.5Zn-xCa (x = 0.5, 1 and 2, in wt.%) alloys without rare earth elements were prepared by conventional extrusion at 360 °C with an extrusion ratio of 25:1. The microstructure evolution and mechanical properties of Mg–5Al–1Mn-0.5Zn-xCa alloys were investigated by OM, XRD, SEM, EBSD, TEM and tensile tests. The as-extruded alloys are almost fine equiaxed grains with dispersed particles (Al2Ca, Al8Mn5, Mg2Ca and nanoscale (Al, Mn)-rich precipitates). With the increase of Ca addition, the average grain size decreases, the fine particles increase and basal textures become stronger, which result that the strength of the extruded alloy increases gradually while the elongation decrease. As-extruded Mg–5Al–1Mn-0.5Zn–2Ca exhibits excellent comprehensive mechanical properties of the ultimate tensile stress (UTS) of 340 MPa and fracture elongation (FE) of 12.8% with fine grains (2.42 μm), strong basal texture, high density of precipitates and dislocations. The TEM results show that Ca and Zn are segregated at the grain boundaries and a large amount of dispersed second-phase particles existed in the Mg–5Al–1Mn-0.5Zn–2Ca alloy, which is beneficial to grain refinement. Besides, the activated nonbasal slips are beneficial to the ductility which result from the restriction of twinning in fine grains and high Schmid factor (SF) of nonbasal slips.

Microstructure, texture, and compressive properties of TC11/TC17 linear friction welded joint at elevated temperatures

The effect of thermomechanical coupling on the microstructure, texture, and compression properties of TC11/TC17 titanium alloy joint prepared by linear friction welding was studied in this work. The results show that the increased temperature decreases the texture density, dislocation density, and deformed grain, but increases the proportions of recrystallization grain and leads to a high Schmid factor. Moreover, more fine martensite α′ phase transforms into the β phase in the TC17 welded zone, and the width of the platelet α′ phase increases slightly in the TC11 welded zone. The β phase has two key slip systems, i.e., {110}<001> and {112}<111>. For the α phase, there are large fractions at approximately 64° and 85°, corresponding to the {112‾2} contraction twin and the {101‾2} extension twin. As compared to the TC17 side, less deformation occurs along the TC11 side. In addition, the compression strength decreases significantly, and the microhardness values of the joint decline gradually with the increase in temperature.

In situ characterisation of the strain fields of intragranular slip bands in ferrite by high-resolution electron backscatter diffraction

High angular resolution electron backscatter diffraction has been used to quantify the local elastic field at the tip of mechanically loaded intragranular slip bands observed in situ in the ferrite grains of an age-hardened duplex stainless steel (Zeron 100). The surface elastic strain field was integrated to calculate in-plane and out-of-plane surface displacements. This allowed the elastic fields to be parameterised in a finite element analysis, which used the displacement field as the boundary conditions, to obtain the potential strain energy release rate (J-integral) and three-dimensional stress intensity factors (KI,II,III).This new analysis method is demonstrated by examining the elastic fields around the tip of an incipient slip band, an array of slip bands and the loading of a slip band. Direct measurement of the stress tensor in the grain identified the active slip systems with the highest Schmid factor. The stress intensity factors ahead of the slip band, measured under load, were directly affected by the magnitude of loading and the inclination angle of the slip band to the observed surface.

Creep anisotropy characteristics and microstructural crystallography of marine engineering titanium alloy Ti6321 plate at room temperature

The anisotropy of the mechanical properties of high-performance titanium-alloy plates has always been a key challenge in the fabrication of alloy plates and the application of components in service. In this work, the room-temperature creep behavior and microstructural crystallography of Ti6321 alloy plates along the rolling direction (RD), 45°, and transverse direction (TD) have been thoroughly investigated and discussed. The study demonstrates that the plates exhibit significantly different room-temperature creep characteristics along the three sampling directions. Among them, the creep strain along the 45° direction was the largest, whereas the creep strain along the TD was the smallest. Such anisotropic deformation was associated with the global Schmid factor variation caused by the T-type microtexture. Both the basal and prismatic slips occur easily along 45°, whereas it was hard to activate along the TD. In addition, the basal and prismatic slips were the main contributors to creep deformation, which also showed strong crystallographic orientation dependence. Among them, the basal slip was found to be more easily activated than prismatic slip, especially in the high Schmid factor range. The study also discusses the potential influence of elastic anisotropy on the activation of basal slip.

Twinning–Detwinning Deformation Mechanism in Ti–15Mo Alloy and Its Effect on the Microstructure Evolution and Yield Strength

{332}&lt;113&gt; twinning is an important deformation mode for metastable β–Ti alloys. However, little is known on the reverse detwinning process and its hardening effect. Herein, detwinning behavior in Ti–15Mo alloy and its effect on the microstructure evolution and yield strength is investigated. Twins are generated during pre‐tension along the rolling direction. Then, the pre‐twinned samples are compressed in the same direction by different strains. It is shown that compressive yield strength is significantly improved by pre‐tension compared with the as‐received alloy. Microstructure characterization reveals that almost all the twins generated in pre‐tension were detwinned during the reverse compression. New twins appear in some β grains by increasing the compression strain. The variant with the highest Schmid factor (SF) is likely selected for twinning. Some paired twins formed at grain boundaries do not have the highest SF, but have a large strain compatibility factor (m′), implying a strong influence from local stress. Profuse slip traces are observed, which transferred across the detwinned regions during the reverse compression, causing severe stress concentrations in the primary twin domains. Based on the experimental observations, a possible strengthening mechanism by the twinning–detwinning behavior is proposed and discussed.

Effects of microstructure and temperature on short fatigue crack propagation behaviour of powder metallurgy superalloy FGH4098 in vacuum

Short fatigue crack propagation (SFCP) behaviour of a powder metallurgy (PM) superalloy (i.e. FGH4098) for aeroengine turbine disc application was investigated at room temperature and 650 °C in vacuum (10−3 pa) by in-situ fatigue test. The SFCP mechanism was analyzed by the microstructural characterization and assessment of the SFCP rate. The results show that the SFCP resistance of fine grained (FG) FGH4098 is slightly better than that of coarse grained (CG) FGH4098 at room temperature due to the hindering effects of grain boundary, and close to that of CG FGH4098 at 650 °C. The temperature exerts more evident influence on SFCP behaviour of FG FGH4098 due to the grain boundary oxidation compared with that of CG FGH4098. In the scenario which grain boundary oxidation is absent or insignificant, SFCP shows transgranular feature and is closely related to slip bands linked to the slip systems with high Schmid factor and/or geometric compatibility factor. Grain boundary oxidation still occurs in both FG and CG FGH4098 alloy and mainly forms Cr oxides at 650 °C, which results in intergranular or mixed-inter-transgranular SFCP and promotes SFCP to some extent for FG FGH4098 alloy.

Simultaneously Improving Ductility and Stretch Formability of Mg-3Y Sheet via High Temperature Cross-Rolling and Subsequent Short-Term Annealing.

In this work, Mg-3Y sheet was prepared by high temperature cross-rolling and subsequent short-term annealing. The effect of annealing on microstructure, texture, mechanical properties, and stretch formability of Mg-3Y sheet was primarily investigated. Micro-nano size coexistence of β-Mg24Y5 phases can be well deformed with matrix. The as-rolled Mg-3Y sheet exhibited a homogeneous deformation microstructure consisting of deformed grains with extensive kink bands and dispersed β-Mg24Y5 phases. A double peak texture character appeared in as-rolled Mg-3Y sheet with a split of the texture peaks of about ±20° tilted to rolling direction. After annealing, the as-annealed Mg-3Y sheet presented complete static recrystallized (SRXed) microstructure consisting of uniform equiaxed grains. The texture orientation distribution was more dispersed and a weakened multiple-peak texture orientation distribution appeared. In addition, the maximum intensity of basal plane decreased from 5.2 to 3.1. The change of texture character was attributed to static recrystallization (SRX) induced by kink bands and grain boundaries. The as-annealed Mg-3Y sheet with high Schmid factor (SF) for basal <a> slip, prismatic <a> slip, pyramidal <a> slip, and pyramidal <c+a> slip exhibited high ductility (~25.6%). Simultaneously, enhanced activity of basal <a> slip and randomized grain orientation played a significant role in decreasing anisotropy for the as-annealed Mg-3Y sheet, which contributed to the formation of high stretch formability (~6.2 mm) at room temperature.

Dynamic recrystallization behavior and strengthening mechanism of quasi-precipitate-free dilute Mg–Bi–Sn alloy

In this study, a dilute Mg–0.5Bi–0.5Sn alloy system was designed and subjected to extrusion at a low temperature of 250 °C. The dynamic recrystallization behavior and strengthening mechanism of the extruded alloy were discussed in detail. At the initial stage of the extrusion process, the dynamic recrystallized grains were formed through twinning-induced dynamic recrystallization (TDRX), continuous dynamic recrystallization (CDRX) and discontinuous dynamic recrystallization (DDRX). In the middle stage of extrusion, the emergence of CDRX and DDRX were synergistic. In the later stage of extrusion, DDRX and CDRX were exclusive and DDRX was the dominant mode. For the dilute extruded Mg–0.5Bi–0.5Sn alloy, the ultimate tensile strength, tensile yield strength and elongation were 282 MPa, 212.4 MPa and 36.3%, respectively, reaching an excellent high strength-ductility balance. The enhanced strength has been an outcome resulting from grain boundary strengthening and texture strengthening, along with dislocation strengthening. Ductility enhancement is closely related to the easily activation of <c+a> slips, which can be ascribed to the relatively high Schmid factor.

Texture evolution during sub-critical annealing and its effect on yield strength anisotropy of laser directed energy deposited Ti-6Al-2Zr-1Mo-1V alloy

Titanium alloys fabricated by laser directed energy deposition (LDED) are usually subjected to sub-critical annealing to improve mechanical properties. This work mainly investigated the texture evolution of LDEDed Ti–6Al–2Zr–1Mo–1V alloy during sub-critical annealing and its effect on the anisotropy of yield strength. Results indicated that <0001> of α phase in the as-deposited sample exhibited two types of circle-shaped texture, which were perpendicular to the deposition direction (VD) and 45° away from VD, respectively. The intensities of these two types of texture were approximately equal because the α texture in the as-deposited sample were transformed from the strong <001>β//VD fiber texture following Burgers orientation relationship with weak variant selection. During sub-critical annealing, the formation of primary α phase, which tended to be transformed from the {110}β parallel to VD, led to the intensity of circle-shaped texture perpendicular to VD greater than that 45° away from VD. The calculation results suggested that all basal and prismatic slip systems of some α variants transformed from the {110}β parallel to VD were in hardly-activated orientation with Schmid factor (m) equal to zero for loading along the horizontal direction (HD), the slip systems of some α variants transformed from the {110}β 45° to VD were in hardly-activated orientation with m = 0 for loading along 45° direction (OD), while the systems of all α variants were in easily-activated orientation with high Schmid factors for loading along VD. After sub-critical annealing, the content of α phase in hardly-activated orientation increased for loading along HD but decreased for loading along OD, resulting in a smaller difference of yield strength between OD and VD or HD.