High-Resolution Digital Image Correlation Analysis of Layered α/β Two-Phase Ti–12Mo Alloy under Compressive Condition

Junyu Zhu; Fabien Briffod; Takayuki Shiraiwa; Manabu Enoki; Satoshi Emura

doi:10.2320/matertrans.MT-M2023111

Abstract

To introduce kink deformation into a titanium alloy, a α/β two-phase Ti–12Mo alloy with a layered structure was developed through a series of thermal-mechanical treatments. The deformation kink bands were generated during uniaxial compression tests. Strain field maps of the kink-favored grain were plotted based on high-resolution digital image correlation (HR-DIC) analysis. The observed kink deformation occurred near the triple point and was significantly influenced by intergranular deformation of the adjacent grain. In grains without kink deformation, the deformation primarily exhibited in the form of slip lines with the same direction as the α phase interface. A crystal plasticity finite element model was developed using electron backscatter diffraction (EBSD) measurements to evaluate the equivalent strain field maps and von Mises stress maps. The grain with kink deformation exhibited low plastic activity and high von Mises stress.

1. Introduction

In the pursuit of addressing the global challenge of climate change, titanium and its alloys have received significant attention due to their superior characteristics of high specific strength and corrosion resistance.¹⁾ Titanium consists of two primary phases: the α phase with a hexagonal close-packed (HCP) crystal structure and the β phase with a body-centered cubic (BCC) crystal structure. In the α phase, the coexistence of $\{ 0001\} \langle 1\bar{2}10\rangle $ basal slip, $\{ 10\bar{1}0\} \langle 1\bar{2}10\rangle $ prismatic slip, $\{ 10\bar{1}1\} \langle 1\bar{2}10\rangle $ pyramidal ⟨a⟩, and $\{ 10\bar{1}1\} \langle 2\bar{2}\bar{1}\bar{3}\rangle $ pyramidal ⟨c + a⟩ slip has been reported.²^,³⁾ On the other hand, the deformation mechanism of the β phase is dependent on its stability, which is controlled by the chemical composition.⁴⁾ In different types of metastable β phase titanium alloys, deformation slip with the same direction ⟨111⟩_β,⁵⁾ {332}⟨113⟩, {112}⟨111⟩ twinning,⁶^,⁷⁾ stress-induced martensitic transformation to α′-martensite phase, and orthorhombic α′′-martensite phase⁸^,⁹⁾ are commonly observed.

Achieving accurate and precise control over the activation of deformation mechanisms has become a popular topic in the field of materials engineering. Studies have been conducted on titanium alloys to assess the formation of kink deformation. In the α phase titanium, the $\{ 11\bar{2}1\} $ twins with only dislocation motion through basal slip can be considered as kink bands.¹⁰^,¹¹⁾ In the β phase of titanium, which has more operative slip systems, it has been reported that a high strain rate is a crucial condition for introducing kink deformation in the alloy.¹²⁾ Three types of kink bands have been identified in β phase titanium alloys after high strain rate compression.¹²^–¹⁴⁾ In general, kink deformation is not a common deformation mechanism in titanium alloys. Inspired by the kink deformation observed in LPSO/Mg alloy,¹⁵^–¹⁷⁾ a series of α/β two-phase alloys with a layered structure similar to the lamellar structure of Mg/LPSO alloys has been developed to introduce kink deformation.¹⁸⁾ In previous research, the mechanical properties of one of the α/β two-phase titanium alloys, Ti–12Mo, were examined by Briffod et al.¹⁹⁾ During the solid-state transformation stage, a preferred Burgers orientation relationship (BOR) exists between the α/twin interface and α/matrix interface. Consequently, the α phase precipitates on the {332}⟨113⟩ β twin boundaries with a fixed orientation, forming a layered structure with the β matrix. Although the precipitated α phase reduces the mean free path, no kink deformation was observed in the compressed Ti–12Mo specimens. In the LPSO/Mg alloy, due to the high plastic anisotropy, it is reported feasible to control the generation of the kink bands by manually defining the loading direction.¹⁷^,²⁰⁾ By aligning the compression direction with the lamellar direction, the {110}_β-rotation-type kink bands were introduced to the two layered two-phase titanium alloys, Ti–10Cr and Ti–9Cr, under compressive conditions.²¹^,²²⁾ It is proposed that the formation of kink bands is initiated by prismatic ⟨a⟩ dislocations. Holding the view that a layered structure is favored for kink deformation, the thermal-mechanical treatment of the Ti–12Mo alloy is modified to introduce a finer layered grain structure with a more lamellar-like microstructure.

In this study, uniaxial compression tests are carried out on the modified Ti–12Mo alloys to induce kink deformation. During the mechanical tests, high-resolution digital image correlation (HR-DIC) is applied to the Ti–12Mo specimens to reveal the in-plane deformation on the surface and quantitatively map the local strain fields.²³^–²⁵⁾ Additionally, a crystal plasticity (CP) model of Ti–12Mo is constructed using electron backscatter diffraction (EBSD) measurements in the crystal plasticity finite element method (CPFEM) software Abaqus. The uniaxial compression tests are simulated using the CP model to gain a comprehensive understanding of the HR-DIC analysis.

2. Material and Methods

2.1 Material

Following a similar process to the previous treatment,¹⁹⁾ the Ti–12Mo (mass%) was melted using the cold crucible levitation melting (CCLM) method to ensure a uniform chemical composition and minimal contamination in the resulting 70 mm-thick ingot. The ingot was then hot forged into a 40 mm-thick square slab at 1273 K and hot rolled at 1173 K to obtain a 6 mm-thick plate. After the air cooling process, the plate underwent a 5-hour solution treatment at 1173 K to generate coarse equiaxed β grains. In contrast to the previous treatment, the plate surface was polished, and a 5% reduction ratio cold rolling was performed in a liquid nitrogen environment. The cold rolling direction was orthogonal to the hot rolling direction to introduce β twins. Furthermore, the thermo-mechanical treatment was completed with a 50-hour aging process, during which the temperature was increased from 923 K to 973 K to precipitate the α phase. The resultant microstructure and crystallographic features of the α/β two-phase Ti–12Mo alloy were characterized using optical microscopy (OM), scanning electron microscope (SEM) observation, and EBSD analysis.

2.2 Experimental procedure

Rectangular specimens with dimensions of 6 × 6 × 6 mm³ were mechanically cut from the treated Ti–12Mo plate. Based on previous studies on kink deformation in grains with a layered structure, it is hypothesized that kink deformation is favored when the loading direction is parallel to the lamellar direction.²²^,²⁵⁾ Before conducting the mechanical tests on the Ti–12Mo specimens, the surface microstructure was examined using OM. The sample surface was polished with emery paper and chemically polished with Kroll’s reagent solution to reveal the surface microstructure. Possible kink grains, whose lamellar direction was parallel to the loading direction, were selected and labeled for HR-DIC analysis. EBSD measurements were performed on each possible kink grain to generate phase maps and crystallographic orientation maps. The accelerating voltage and probe current were set to 20 kV and 16 mA, respectively, with a step size of 0.3 µm. Uniaxial compression tests were conducted on the Ti–12Mo specimens at room temperature using an Autograph AGS-100kNXplus (Shimadzu) with a constant displacement rate of 0.005 mm/s. A full compression test with a plastic strain of over 25% was initially applied to obtain a complete stress-strain diagram. The strain during the compression tests was estimated based on the applied force and corresponding cross-sectional area using the obtained stress-strain curve. Subsequent compression tests on the Ti–12Mo specimens were interrupted at approximately 4% strain intervals, and SEM images were acquired in backscattered electron imaging (BEI) mode at a magnification of 2000× after unloading. The acceleration voltage was set to 15 kV, with a probe current of 10 mA and a working distance of 10 mm. High-resolution digital image correlation analysis was performed on the surface of the compressed Ti–12Mo specimens at different deformation stages. EBSD measurements were carried out on the possibly kinked grain after deformation and analyzed using the open-source software MTEX for MATLAB.²⁶⁾

2.3 High-resolution digital image correlation

Although the DIC analysis based on SEM/EBSD observation has already yielded good in-plane strain fields, achieving high-resolution digital image correlation requires creating recognizable microstructure-independent patterns. Each region should contain sufficient features that can be easily identified in the subsequent image. To introduce these recognizable features at different deformation stages, a speckle pattern was implemented using the vapor-assisted remodeling of metal nano-film method.²⁷⁾ The schematic of the vapor-assisted remodeling of the gold nano-film method is depicted in Fig. 1. A 10-nm-thick gold film was deposited onto the Ti–12Mo specimen surface using an ion sputtering device, JFC-1500 (Jeol). Subsequently, the coated specimen was placed on a 300°C hot plate in a saturated water vapor environment for 1.5 hours. This high-temperature environment with saturated water vapor prevented condensation on the specimen surface and facilitated the clustering of undesirable large gold patterns.²⁸⁾

Fig. 1

Schematic of vapor-assisted remodeling of gold nano-film.²⁸⁾

Ex-situ SEM observations were conducted on the labeled possible kink grains with gold nanoparticle deposition at a magnification of 2000× with a resolution of 1280 × 960. Different numbers of SEM figures were taken based on the size of the labeled grains, with an overlap of 10% between neighboring pictures. The obtained SEM figures were stitched together using the software ImageJ (Fiji).²⁹⁾ The strain field was calculated and analyzed using the SEM figures in MATLAB with the open-source software Ncorr.³⁰⁾ Figure 2(a) displays an SEM image with a magnification of 5000×, showing the formation of large bright gold islands inside the dark α phase. For the deformed specimen, the magnification of the SEM observation was set to 2000×, as shown in Fig. 2(b). The subset size for the HR-DIC analysis was set to 10 pixels, equivalent to 465 nm. A step size of 1 pixel was selected to ensure accuracy. To calculate the in-plane strain field maps, a bilinear interpolation of the displacement field was implemented with a strain radius of 3 pixels.

Fig. 2

SEM image of the Ti–9Cr sample for DIC analysis with BEI mode under (a) 5000× magnification; (b) 2000× magnification.

2.4 Numerical methods

Uniaxial compression tests were simulated in the commercial finite element software Abaqus with a user-material subroutine (UMAT).³¹⁾ The single crystal kinematics can be described with the multiplicative decomposition of the deformation gradient³²⁾

\begin{equation} \text{F} = \text{F}^{e}\text{F}^{p} \end{equation}

(1)

The total deformation gradient tensor F is decomposed into the elastic part representing the stretching and rigid-body rotation F^e and plastic deformation gradient F^p. The plastic deformation gradient rate $\dot{\text{F}^{p}}$ can be defined with the plastic velocity gradient L^p

\begin{equation} \dot{\text{F}^{p}} = \text{L}^{p}\text{F}^{p} \end{equation}

(2)

where the magnitude and direction of the plastic velocity gradient L^p is equivalent to the summation of the shear rate on all of the slip systems³³⁾

\begin{equation} \text{L}^{p} = \mathop{\Sigma}\nolimits_{\alpha = 1}^{N_{s}}\dot{\gamma^{\alpha}}\mathbf{m}^{\alpha} \otimes \mathbf{n}^{\alpha} \end{equation}

(3)

where m^α and n^α represents the slip direction and slip plane normal direction respectively. A phenomenological model using the critical resolved shear stress as its state variable for individual slip systems was used in this study. The resolved shear stress γ^α is given as:

\begin{equation} \gamma^{\alpha} = \mathbf{S}:\mathbf{m}^{\alpha} \otimes \mathbf{n}^{\alpha} \end{equation}

(4)

The plastic shear rate $\dot{\gamma^{\alpha}}$ can be calculated with a function of the resolved shear stress with the power-law³⁴^–³⁶⁾

\begin{equation} \dot{\gamma^{\alpha}} = \dot{\gamma_{0}}\left|\frac{\tau^{\alpha}}{\tau_{c}^{\alpha}}\right|^{n}\mathit{sgn}(\tau^{\alpha}) \end{equation}

(5)

where $\dot{\gamma_{0}}$, τ^α, $\tau_{c}^{\alpha }$, and n represent the reference shear strain rate, resolved shear stress on the slip system α, slip resistance, and strain rate sensitivity exponent,³⁷⁾ respectively. The S stands for the second Piola–Kirchhoff stress tensor, the equation is given as

\begin{equation} \mathbf{S} = \mathbb{C}:\mathbf{E}_{\boldsymbol{e}} \end{equation}

(6)

where $\mathbb{C}$ and E_e represent the fourth-order elastic stiffness tensor, and Green-Lagrange elastic strain tensor, respectively. The slip resistance $\tau_{c}^{\alpha }$ is given as:

\begin{equation} \tau_{c}^{\alpha} = \tau_{0}^{\alpha} + \tau_{1}^{\alpha}(1 - e^{-\frac{b_{1}^{\alpha}}{\tau_{1}^{\alpha}}\Gamma_{s}}) \end{equation}

(7)

where $\tau_{0}^{\alpha }$ is the initial CRSS, $\tau_{0}^{\alpha } + \tau_{1}^{\alpha }$, $b_{1}^{\alpha }$ and Γ_s represents the saturated CRSS, initial hardening rate, and total accumulated shear strain, respectively.

The CPFE models of the selected possible kink grains were generated by directly converting the captured EBSD data.³⁸⁾ The converted EBSD model was divided into 1,000,000 elements, with 1,000 elements in both the x-direction and y-direction. A boundary condition was applied to the converted 2D model, fixing the bottom face in all directions and preventing rotations.

The elastic constants for the α phase titanium proposed by Simmons³⁹⁾ and for the β phase titanium proposed by Kim and Rokhlin⁴⁰⁾ were listed in Table 1. Furthermore, the calibrated crystal plasticity parameters, as shown in the previous report,²²⁾ were introduced to the CP simulation and listed in Table 1.

Table 1 Elastic constants and crystal plasticity parameters for the layered α/β two-phase titanium alloys.

3. Results and Discussion

3.1 Microstructures

The OM figure of the Ti–12Mo alloy is shown in Fig. 3(a). The size of the recrystallized coarse equiaxed β grains varied around several hundred µm. EBSD measurements were conducted on a single grain with a fine layered structure. The inverse pole figure (IPF) maps of the single α phase and single β phase are listed in Fig. 3(b) and Fig. 3(c), respectively. A layered structure with alternately stacked α and β phases was observed. The precipitated α phase exhibited an average thickness of several hundred nanometers, while the β twins had a thickness of 2–3 µm, dividing the β matrix into layers of about 10 µm. The directions of the α precipitates, β twins, and β matrix were projected in Fig. 3(d). The projection of the (0001) α plane overlapped with one of the projections of the {110} β plane for both the β twins and the matrix. Additionally, one projection of the $\langle 1\bar{2}10\rangle $ α direction was overlapped with the ⟨111⟩ β direction for the β matrix, while another projection of the $\langle 1\bar{2}10\rangle $ α direction was overlapped with the ⟨111⟩ β direction for β twins. Therefore, during the solid-state transformation, the same Burgers orientation relationship (BOR) variant was preferred at both the α/β matrix interface and the α/{332}⟨113⟩ β twins interface. One of the common {110} planes was shared by the nucleated α phase and the neighboring β twin and matrix. The β phase misorientation map was calculated and plotted in Fig. 3(e) to distinguish the formed β twins. A uniform misorientation angle of 50.5° was revealed, indicating that the formed β twins were {332}⟨113⟩ β twins. The cold rolling process in a liquid nitrogen environment led to a notable increase in the number of formed β twins. As a result of the increased amount of β twins, which provided suitable precipitation locations for the α phase, the grain exhibited a finer layered structure with the modified thermal-mechanical treatment.

Fig. 3

(a) Optical micrograph of the Ti–12Mo specimen, (b) IPF map of α phase, (c) IPF map of β phase, (d) Stereographic projections of β matrix/twin {110} planes and ⟨111⟩ directions, α precipitates (0001) plane and $\langle 1\bar{2}10\rangle $ directions, color represents the IPF color of the corresponding orientation in the EBSD map; (e) β phase misorientation map of Ti–12Mo sample.

3.2 Mechanical behavior

The surface of the deformed specimen after the uniaxial compression test was observed using OM, and the resulting OM figure is shown in Fig. 4(a). The stress-strain curve is plotted in Fig. 4(b), with the yield stress of the Ti–12Mo alloy measuring around 900 MPa. Among the deformed grains, three grains exhibiting potential kink deformation were identified and marked in the central-right part of the specimen. These grains were observed at a higher magnification, and the corresponding figures are depicted in Fig. 4(c)–(e). Their layered lamellar structures exhibited a distinct zigzag morphology, with potential kink boundaries highlighted with red lines. In all three grains, the deformation bands were found to initiate near the triple point and propagate across the entire grain. The lamellar directions were nearly parallel to the loading direction, with the largest inclination observed in Fig. 4(c), where the lamellar direction was approximately 35° inclined to the loading direction.

Fig. 4

(a) OM figure of Ti–12Mo specimen after deformation with possible kink grains labeled; (b) Stress-strain (σ-ε) curve; (c), (d), (e) OM figures of the possible kink grains I, II, and III with higher magnification.

To assess and analyze the crystallographic characteristics of the formed deformation bands, EBSD measurements were performed on the selected grains. The obtained IPF maps of the three grains with potential kink deformation are presented in Fig. 5(a)–(c) and Fig. 5(g)–(i). Due to the large deformation of the specimen, the EBSD results inside the kink bands were poorly indexed. In each grain with potential kink deformation, a red-highlighted profile path was selected to identify the lattice rotation axis. The (0001)_α, $(10\bar{1}0)_{\alpha }$, (110)_β, and (111)_β pole figures of the selected profile path with the corresponding phase were plotted in Fig. 5(d)–(f) and Fig. 5(j)–(l). Owing to the lack of indexed crystals within the kink band, the projections of the profile were scattered in a relatively uniform manner in all of the planes. It was thus challenging to distinguish the crystal rotation axes accurately. To determine the crystal rotation axis, instead of following a single profile, large areas inside the grains with potential kink deformation, which contained the formed possible kink bands were selected. Probability density maps for crystal rotation axis of the selected regions were then plotted.

Fig. 5

α phase Z direction IPF coloring orientation map for (a) possible kink grain I; (b) possible kink grain II; (c) possible kink grain III; (d), (e), (f) Pole figures of the corresponding deformed α phase; β phase Z direction IPF coloring orientation map for (g) possible kink grain I; (h) possible kink grain II; (i) possible kink grain III; (j), (k), (l) Pole figures of the corresponding deformed β phase.

In the zinc single-crystal model proposed by Hess and Bert, the compression direction was set to align with the basal plane, which prohibited the occurrence of twinning deformation.⁴¹⁾ In the following studies on kink deformation in LPSO/Mg alloys, it was suggested that kink deformation was initiated by the accumulation of basal slip.²⁵⁾ Different from the LPSO/Mg alloys whose prismatic slip was not an active deformation mechanism, the prismatic slip was revealed as an active deformation mechanism in the Ti–12Mo alloy in the previous study.¹⁹⁾ It was therefore proposed that the activated prismatic slip hindered the kink band formation. Nonetheless, the ⟨0001⟩ rotation-type of kink bands initiated by prismatic ⟨a⟩ slip were reported in the LPSO/Mg alloy,⁴²⁾ and the {110}_β-rotation-type kink bands initiated by prismatic ⟨a⟩ slip were revealed in the layered α/β two-phase Ti–9Cr and Ti–10Cr alloys.²¹^,²²⁾ According to the OM images listed in Fig. 4(c)–(e), buckling-like morphology was located in the Ti–12Mo alloys with modified thermal-mechanical treatment. The grains exhibiting potential deformation kink bands showed a lamellar direction aligned with the loading direction. In Fig. 5(d)–(f), the α phase stereographic projections of the three grains exhibited a similar distribution. Interestingly, the crystal projections on the basal (0001) plane were scattered around the y-axis. Since the compression direction was along the y-axis, the c-axis of the α phase was found to be nearly parallel to the loading direction in all grains with kink deformation. To identify the crystal rotation axis, probability density maps of the crystal rotation axis were plotted. As shown in Fig. 5(k), the potential crystal rotation axis with the highest probability overlapped with one of the six (110) common planes, indicating that the crystal rotation axis was parallel to one of the (110) normals. The presence of {110}_β-rotation-type kink bands was revealed in the Ti–12Mo alloy.

3.3 HR-DIC analysis

Prior to the uniaxial compression tests, the microstructures of the Ti–12Mo specimens were examined using EBSD measurements to record the crystallographic features. Two grains were selected for the HR-DIC analysis, and the obtained IPF maps are shown in Fig. 6(a) and Fig. 6(b). It was observed that both selected grains exhibited layered lamellar structures. The compression direction was along the y-direction. Therefore, the first selected grain had a lamellar direction that was almost parallel to the loading direction, while the second grain had an inclination angle of approximately 30° with respect to the loading direction.

Fig. 6

IPF map of the selected Ti–12Mo grains before the deformation.

In the first specimen, the compression was first interrupted after reaching a yield point of approximately 2.5% plastic strain. Subsequent mechanical tests were interrupted at 7%, 10%, 13%, and 20% plastic strain. The calculated equivalent strain field maps are presented in Fig. 7(b)–(f). Strain localizations were observed in the top left and bottom left triple points of the grain and propagated with the increase of the plastic strain. Small kink bands with a zigzag morphology were observed and highlighted around the bottom-left triple point. The equivalent strain field maps for the kink bands are shown in Fig. 7(g)–(k).

Fig. 7

(a) Stitched SEM image of the selected grain No. 1 before deformation; Stitched equivalent strain field maps calculated from DIC analysis after; (b) 2.5% plastic strain; (c) 7% plastic strain; (d) 10% plastic strain; (e) 13% plastic strain; (f) 20% plastic strain; Enlarged equivalent strain field maps after (g) 2.5% plastic strain; (h) 7% plastic strain; (i) 10% plastic strain; (j) 13% plastic strain; (k) 20% plastic strain.

According to the equivalent strain field map depicted in Fig. 7(b), two distinct strain localizations were observed at the top left and bottom left triple points. Noticeable plastic deformation accumulated along the grain boundaries. With the increase of the applied stress, it became evident that the strain localization at the top left triple point formed a shear band and propagated across the grain along the direction of the grain boundary. Meanwhile, around the bottom left triple point, the lamellar structure was significantly influenced by the intergranular deformation of the adjacent grain. It was observed that sharp strain localization occurs in the form of intergranular deformation once the deformation exceeds the yield point of 2.5% plastic strain. After applying 10% plastic strain to the specimen, the introduced deformation bands exhibited a buckling-like morphology, forming the deformation kink bands. The further increase in applied strain was accommodated by the broadening of the formed kink bands.

For the second selected grain, an interval of approximately 5% plastic strain was applied during the uniaxial compression tests. The mechanical tests were interrupted at 5% and 10% plastic strain, and eventually terminated at a 12% plastic strain. The obtained equivalent strain field maps are displayed in Fig. 8(b)–(d).

Fig. 8

(a) Stitched SEM image of the selected grain No. 2 before deformation; Stitched equivalent strain field maps calculated from DIC analysis after; (b) 5% plastic strain; (c) 10% plastic strain; (d) 12% plastic strain.

In this specimen, strain localizations were exhibited at the α phase interface, and no kink deformation was observed. Instead, a significant number of slip lines parallel to the α phase interface were observed during the uniaxial compression process. Although a 12% global strain was applied to the specimen, a relatively low local strain was observed in the selected grain. It is thus believed that further deformation was hindered.

Although the formation mechanism of kink deformation is still vague, it is believed to be strongly related to the generation of a large number of dislocations. The deformation kink bands are the results of the accumulation and alignment of the generated dislocations. Such accumulation of dislocations would inevitably create local inhomogeneous plastic areas.⁴³⁾ In the equivalent strain field maps of the selected grain No. 1, such local inhomogeneous plastic areas were observed as sharp strain localization at the bottom left triple point, indicating the formation of kink bands. On the other hand, in the selected grain No. 2, the strain was uniformly distributed along the α phase interface without any local strain concentrations. In this scenario, the dislocations traveled freely along the α phase interface without obstruction, making it impossible to trigger kink deformation.

3.4 Numerical results

A custom-made MATLAB script was developed to convert the acquired EBSD data of the first and second selected grains into CPFE models. Uniaxial compression tests were conducted on the two models, applying a 13% plastic strain. In order to make a visual comparison between the experimental and numerical results, strain field maps and von Mises stress maps were simulated and plotted at 5%, 10%, and 12% of plastic strain, as shown in Fig. 9 and Fig. 10. No kink deformation was observed in either of the models after reaching 12% plastic strain.

Fig. 9

Simulated strain field maps on the selected grain No. 1 after (a) 5% plastic strain; (b) 10% plastic strain; (c) 12% plastic strain; von Mises stress maps after (d) 5% plastic strain; (e) 10% plastic strain; (f) 12% plastic strain.

Fig. 10

Simulated strain field maps on the selected grain No. 2 after (a) 5% plastic strain; (b) 10% plastic strain; (c) 12% plastic strain; von Mises stress maps after (d) 5% plastic strain; (e) 10% plastic strain; (f) 12% plastic strain.

Based on the experimental results, the developed Ti–12Mo CP models can be categorized into two groups: grains well-oriented for kink deformation and grains poorly oriented for kink deformation. For the grains well-oriented for kink deformation, strain localizations were observed inside the neighboring grain with little influence on the grain of interest, as shown in the equivalent strain field maps in Fig. 9(a)–(c). Figure 9(d)–(f) displayed a relatively high von Mises stress during the deformation process. On the other hand, for the grains poorly oriented for kink deformation, Fig. 10(d)–(f) demonstrated a low von Mises stress compared to the previous simulation results. The grain of interest mainly deformed in the form of slip lines parallel to the α phase interface. Therefore, in the simulation, the dislocations were able to travel freely in the converted CP models without obstruction. Although the grains well-oriented for kink deformation exhibited a relatively high von Mises stress, it was still impossible to initiate kink deformation without the accumulation of dislocations. These findings from the simulation were consistent with the experimental results.

In general, kink deformation is not a common deformation mechanism in layered α/β two-phase titanium alloys. Further study is required to understand the mechanism of the impediment effect on dislocation motion.

4. Conclusion

A combination of experimental and numerical approaches, using high-resolution digital image correlation and crystal plasticity finite element method, was conducted to investigate the plastic deformation of a layered α/β two-phase Ti–12Mo alloy under compressive conditions. Based on the aforementioned findings, the main conclusions can be summarized as follows:

(1) {110}_β-rotation-type kink bands were successfully introduced to the layered α/β two-phase Ti–12Mo alloy with modified thermal-mechanical treatment. In all of the grains with kink deformation, the c-axis of the α phase was nearly parallel to the loading direction.
(2) In grains with kink deformation, the kink band was always initiated near the triple point. Due to intergranular deformation of the adjacent grain, the deformation kink bands were formed and propagated during the deformation process. In grains without kink deformation, slip lines parallel to the α phase interface were commonly observed.
(3) Uniaxial compression tests were simulated on the two CP models converted from the EBSD data. The model representing the grain well oriented for kink deformation exhibited limited plastic activity and high von Mises stress. The other model representing the grain poorly oriented for kink deformation showed limited von Mises stress, with deformations mainly in the form of slip lines parallel to the α phase interface.

REFERENCES

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