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Article

Characterization and Analysis of Strain Heterogeneity at Grain-Scale of Titanium Alloy with Tri-Modal Microstructure during Tensile Deformation

1
State Key Laboratory of Solidification Processing, Shaanxi Key Laboratory of High-Performance Precision Forming Technology and Equipment, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi’an 710072, China
2
School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an 710129, China
*
Authors to whom correspondence should be addressed.
Materials 2018, 11(11), 2194; https://doi.org/10.3390/ma11112194
Submission received: 11 October 2018 / Revised: 30 October 2018 / Accepted: 2 November 2018 / Published: 6 November 2018
(This article belongs to the Section Advanced Materials Characterization)

Abstract

:
Grain-scale strain heterogeneity characteristics play a critical role in the ductile damage behavior and mechanical properties of two-phase titanium alloys. In this work, the grain-scale strain distribution, strain heterogeneity, and strain localization of titanium alloy with tri-modal microstructure (consisting of equiaxed α (αp), lamellar α (αl), and β transformed matrix (βt)) during tensile deformation were experimentally investigated. The results show that the strain probability distribution of the whole microstructure obeys normal distribution during deformation. Significant strain heterogeneities exist in each constituent (αp, αl, and βt) and the whole microstructure. At lower macro-strain, αp and αl exhibit higher average strain than those of βt and the whole of the microstructure. Meanwhile, strain heterogeneity of each constituent is small and has a negligible change. The strain heterogeneity of the whole microstructure is mainly determined by αp. At larger macro-strain, some highly deformed regions produce and their positions do not change during further deformation. As a result, the strain heterogeneity of each constituent increases fast, and the strain heterogeneity of whole microstructure is mainly related to αl in this deformation stage. On the other hand, two types of strain localization may be generated within αp and αl and at the αpt and αlt boundaries, respectively. The former type is caused by transgranular intense slip deformation and presents crystal orientation dependence. The latter type is related to the boundary sliding and presents spatial distribution dependence for αl. These strain localizations greatly determine the micro-damages, thus forming the corresponding micro-voids within αp and αl and the micro-cracks at αpt and αlt boundaries in tri-modal microstructure at larger deformation.

1. Introduction

Two-phase titanium alloys are widely used in medicine and aviation fields. In the field of medical engineering, they are mainly applied in the form of orthopedic implants and surgical implants, such as the hip implants, knee joints, and substitutions of shoulder, spine, elbow, and hand. In the aviation field, the typical specific application examples include the vane frame, fan disk, landing gears, etc., where excellent microstructure and mechanical properties are required [1,2,3,4,5,6]. Due to the different crystal structures and constituent behavior between constituent phases (the hexagonal close-packed α and the body-centered cubic β), deformations in two-phase titanium alloys are always heterogeneous, which can be characterized by strain heterogeneity [7,8]. Such heterogeneity may lead to incompatible deformation, even strain localization and shear bands, dramatically determining the ductile damage and mechanical properties [9,10,11]. From a microstructural point of view, morphology, volume fraction, size, crystal orientation, and spatial arrangement of each constituent phase all significantly affect the heterogeneity. Therefore, strain heterogeneity is a critical grain-scale phenomenon bridging microstructures and mechanical properties. Deep understanding on strain heterogeneity is essential for optimizing the microstructure and mechanical properties of titanium alloy.
Recently, many experimental and micromechanical modeling investigations have been conducted on the characteristic of grain-level strain heterogeneity and damage behavior of two-phase metals, especially the dual phase (DP) steel. Ghadbeigi et al. [12] studied the local deformation and damage mechanisms of DP600 steel by conducting in-situ deformation and microscopic digital image correlation (DIC). They found that the strain within ferrite phase is much larger than that within martensite, and severe deformation localization often produces within ferrite grains. The failure of martensite occurs mainly due to the micro-crack initiation from boundaries with ferrite, while the failure of the ferrite matrix mainly occurs by void formation within ferrite. By the combination of in-situ experiment and micromechanical simulation coupling damage model, Matsuno et al. [9] found that the martensite fracture and interface decohesion both play great roles in the strain partitioning, strain localization, and the subsequent void growth and coalescence for DP steel. Lai et al. [13] and Jafari et al. [14] investigated the influence of martensite volume fraction and spatial distribution on the strain localization and damage behavior of DP steel, respectively. These works suggest that the strain heterogeneities and failure mechanism of DP steel strongly depend on the morphology, content, size, and distribution of ferrite and martensite.
For two-phase titanium alloy, the morphology, spatial distribution, and disparity of constitutive behavior of constituent phases (α and β phases) are different from those of DP steel (ferrite and martensite), which make it present different rules on the strain heterogeneities and damage behavior. Barkia et al. [15] experimentally investigated the evolution law of strain heterogeneity and formation of highly deformed band in the tensile of commercial purity (CP) titanium. Through the high-resolution digital image correlation, Lunt et al. [16] quantified the strain distribution in both equiaxed α and fine α2 precipitation in the deformation of Ti-64 alloy with equiaxed microstructure. Ji and Yang [17] developed a microstructure-based finite element model to analyze the strain distribution of TA15 alloy with bimodal microstructure under tensile loading, which was found greatly dependent on the volume fraction, spatial distribution, and yield stress of each constituent. Zhang et al. [18] simulated the grain-scale strain heterogeneity and discussed its role in the shear band and vertical split failure during tensile deformation of Ti-64 alloy with equiaxed and bimodal microstructures. Katani et al. [19] developed a micromechanical model coupling the Gurson-Tvergaard-Needleman damage model, by which they predicted the effect of microstructure morphology on strain localization and void nucleation during tensile deformation of Ti-64 alloy with equiaxed microstructure. The informed works mainly focus on the strain heterogeneities of equiaxed and bimodal microstructure, but there is little concern on the tri-modal microstructure consisting of equiaxed α (αp), lamellar α (αl), and β transformed matrix (βt). It has been reported that tri-modal microstructure is a potential microstructure type presenting better combination of strength, fracture toughness, and fatigue property [20]. The more complex constituents and morphology in tri-modal microstructure may lead to more complicated grain-scale incompatible deformation. Therefore, revealing the characteristics of grain-scale strain heterogeneity in tri-modal microstructure is needed.
In this paper, the grain-scale strain distribution of titanium alloy with tri-modal microstructure during tensile deformation was characterized by microscopic DIC technique. Then, the strain heterogeneity characteristics, strain localization mechanism, and its effect on the micro-damage were analyzed. It will deepen the understanding on grain-scale strain heterogeneity and damage behavior of titanium alloy with tri-modal microstructure.

2. Experimental Procedure

2.1. Material and Initial Microstructure

The material used in this work is wrought TA15 titanium alloy provided by Western Superconducting Technologies Co., Ltd. (Xi’an, China). Its chemical compositions (wt%) are as follows: Al: 6.69; Mo: 1.77; V: 2.25; Zr: 2.26; Fe: 0.14; and Ti balance. The measured β-transus temperature is 985 °C. The initial microstructure is a typical equiaxed microstructure, as shown in Figure 1. To obtain a tri-modal microstructure, the processing schedule shown in Figure 2a is employed. The formation mechanism of tri-modal microstructure under this processing schedule has been reported in the author’s previous work in detail [7,21]. Figure 2b shows the obtained tri-modal microstructure, which consists of about 22.6% αp, 21.6% αl, and βt balance. The most striking feature of a tri-modal microstructure is the existence of αl compared to equiaxed and bimodal microstructures.

2.2. Tensile Testing and Mapping of Strain Field

The processed material with tri-modal microstructure was machined to a plate tensile specimen. The detailed geometry and dimensions are shown in Figure 3a. The lengths of whole sample, parallel section, and grasp sections are 54, 20, and 15 mm, respectively. The widths of a parallel section and grasp section are 10 and 5 mm, respectively. The thickness of the sample is 2 mm. The fillet between parallel and grasp sections is 2.7 mm. Before the tensile test, the specimen surface was mechanically and electrolytically polished in a solution of 5% HClO4 + 65% CH3OH + 40% C4H10O for 40 s firstly. The electron beam lithography technique was then employed to print a gold micro-grid with the area of 1 × 1 mm2 at the center (Figure 3a), which wasconducted on a CABL-9000C electron beam lithography system (Crestec corporation, Tokyo, Japan) equipped with the Nanometer Pattern Generation System. The detailed introduction for this technique can be found in [22]. In this work, the line width and mesh size of micro-grid are 0.2 and 1 μm, respectively. After that, the specimen was intermittently stretched to four different engineering macro-strains using a Bairoe tensile testing machine (Bairoe, Shanghai, China) with the strain rate of 0.0001 s−1 at room temperature. The macro-strains were detected by laser extensometer (Epsilon Technology Corp, Jackson, MS, USA) as 1.45%, 2.77%, 4.7%, and 12.75%, respectively. After each tensile stage, the micro-grid in the area of interest (AOI) (Figure 3b) was observed by a scanning electron microscope (Carl Zeiss AG, Oberkochen, Germany).
Subsequently, the strain field in AOI was calculated by correlating the images of deformed grids with the reference image of undeformed state at different macro-strains. The detailed calculating methods are as follows [23]. First, each square in micro-grid was divided into four triangles by two diagonal lines. For each triangle, the coordinates of vertices before and after deformation are defined as ( x 0 1 , y 0 1 ) ,   ( x 0 2 , y 0 2 ) ,   ( x 0 3 , y 0 3 ) and ( x 1 , y 1 ) ,   ( x 2 , y 2 ) ,   ( x 3 , y 3 ) , respectively. The displacement components of each vertex after deformation are
u 1 = x 1 x 0 1 , v 1 = y 1 y 0 1 u 2 = x 2 x 0 2 ,   v 2 = y 2 y 0 2 u 3 = x 3 x 0 3 ,   v 3 = y 3 y 0 3
The displacement ( u i , v i ) of any interior point ( x i , y i ) in each triangle can be represented by Equation (2) based on the liner relationship between them.
u i = a + b x i + c y i v i = d + e x i + f y i
The values of a, b, c, d, e, and f in Equation (2) can be calculated by substituting Equation (1) into Equation (2). The Green-Lagrange strain in two dimensions can be represented by the differential forms of Equation (3):
ε x x = 1 2 ( u i x u i x + v i x v i x ) ε y y = 1 2 ( u i y u i y + v i y v i y ) γ x y = 1 2 ( u i x u i y + v i x v i y ) ε e q = 4 9 ( ε x 2 ε x ε y + ε y 2 ) + 4 3 γ x y 2
where ε i ( i = x x ,   y y ) ,   γ x y   and   ε e q are the average of the total normal strain, the shear strain, and the equivalent strain of each triangle, respectively. Finally, the strain of each square can be obtained by averaging the strains of four triangles within it. The calculation results show that the distributions of axial strain and equivalent strain are very close for all macro-strains due to the unidirectional tensile deformation. Here, the axial strain field in AOI was used to analyze the strain heterogeneity characteristics of the tri-modal microstructure. Moreover, the microstructure graph was superimposed on the strain map to analyze the dependence of strain distribution on microstructure.

3. Results and Discussion

3.1. Characteristics of Strain Heterogeneity

Figure 4 shows the evolution of the axial strain field in the AOI of tri-modal microstructure during tensile tests. From Figure 4a, it can be found that the strain in the whole region is small and distributes relatively uniformly at the early stage of deformation. No obvious strain localization region can be found. As the deformation proceeds, the overall strain level increases a little and the strain starts to preferentially accumulate at some regions, as shown in Figure 4b. When the macro-strain reaches to 4.7%, four highly deformed regions are formed, as indicated by arrows in Figure 4c. They are located within αp and αl and at the αpt and αlt boundaries, respectively. At the subsequent deformation, these highly deformed regions nearly keep in the same locations, while the strain level increases a substantial amount (Figure 4d). The corresponding strain localization mechanisms for four highly deformed regions will be explained in Section 3.2 in detail.
To quantitatively describe the strain distribution characteristics, the probability distribution of strains at grid nodes under different macro-strains are shown in Figure 5. Here, the relative frequency is used to represent the probability of the strain of each point locating in a certain strain range. It is calculated by the following equation:
f i   =   N i / N t o t a l
where Ni is the amount of points locating in the strain Range i, and Ntotal is the total points of the domain. It can be found that the probability distribution of strain at different deformation stages all obey normal distribution (as fitted by black lines). This phenomenon is the same as the normal distribution of strain in CP titanium [15] and magnesium alloy [22], while different to the lognormal distribution of strain in pearlite microstructure [23]. In addition, we can see that the fitted normal distribution curve widens as the deformation proceeds. This indicates that both the strain heterogeneity and average strain of the tri-modal microstructure increase as deformation occurs.
Figure 6 shows the variations of average and standard deviation (STD) of strain in the whole microstructure (WM) and each constituent (αp, αl, and βt). Here, STD is an important index that can evaluate the strain heterogeneity. Overall, there exist two change stages with different rules for both the average and STD of the strain in the whole deformation process. At lower macro-strain (<4.7%), the average strains of αp and αl are close and slightly larger than WM and βt, as shown in Figure 6a. Lei et al. [7] have experimentally investigated the nano-hardness of constituents in tri-modal microstructure and found that the αp and αl are softer than βt at room temperature. Thus, αp and αl are easier to deform than βt and present a larger average strain. Meanwhile, STD of WM and each constituent are all relatively small and present negligible variations in this deformation stage. It is worth noting that STD of αp is much bigger than other constituents, which suggests that αp is mainly responsible for the strain heterogeneity of WM in this deformation stage. At larger macro-strain (≥4.7%), both the average strain and STD of each constituent and WM increase quickly. Moreover, it can be found from Figure 6a,b that the average strain and STD of αl are both obviously larger than other constituents, which is related to the formation of strain localization regions near αl (see Figure 4c,d). On the contrary, αp presents the smallest STD and strain heterogeneity, which may be related to its features of easy-to-deform and superior deformation compatibility. The above results indicate that αl plays a more important role in the strain heterogeneity of WM at larger macro-strain (≥4.7%). It can be concluded that the softer αp and αl in tri-modal microstructure undertakes more deformation and greatly affects the strain heterogeneity in tri-modal microstructure. Similarly, Ji and Yang [17] have found that the strain significantly localizes in softer primary α phase and contribute to the strain heterogeneity in TA15 alloy with bimodal microstructure.

3.2. Strain Localization and Micro-Damage

As mentioned above, four highly deformed regions, i.e., strain localization region, are formed when the macro-strain reaches to 4.7% (Figure 4c). Their formations play great roles in the strain heterogeneity and micro-damage behavior. Thus, in this section, the strain localization mechanisms are discussed by analyzing the corresponding characteristics of grid changes and microstructure morphology after deformation. Moreover, their relations to the micro-damage behavior are also analyzed.
According to the location of strain localization regions (indicated by arrows in Figure 4c), these regions can be classified into two types: Type 1, strain localization within αp and αl; Type 2, strain localization at the αpt and αlt boundaries. Figure 7 shows the local strain distribution and grid change of Type 1 strain localization regions. It can be found that the strain localization corresponds to the obvious grid distortion within αp and αl, as indicated by the ellipses. Meanwhile, quantities of slip lines are found within some αp and αl in the surface of deformed microstructure, as shown in Figure 8. These suggest that the dislocation slip is the main deformation mode within αp and αl; moreover, intense slip deformation within some grains will generate local strain localization (Type 1). Some potential Type 1 strain localization are indicated in Figure 8. We can find that intense slip deformation and Type 1 strain localization only occurs in some particular αp and αl grains. Even for some adjacent grains, only individual grains will produce strain localization. For example, there are two adjacent αp grains in each ellipse in Figure 4c and Figure 8; however, only one of them produces intense slip deformation and strain localization after deformation. This is because the slip deformation within αp and αl are strongly dependent on the crystal orientation, which are easier to take place in soft-oriented αp and αl. Thus, the neighboring grains may present different degrees of slip deformation and strain localization. These indicate that Type 1 strain localization within αp and αl present crystal orientation dependence.
As for Type 2 strain localization, the corresponding strain distribution and grid change are given in Figure 9. Obvious shift and fracture of microgrids are found at the boundaries of αpt and αlt, which implies the boundary sliding occurs in these regions. Barkia et al. [15] have also observed the boundary sliding at αpp boundary during the tensile deformation of CP titanium at room temperature. Similarly, Katani et al. [19] have also reported the shear deformation and fracture along αpt boundary during the tensile deformation of Ti-64 alloy at room temperature. The corresponding mechanism can be inferred from the corresponding features of deformed microstructure (Figure 8) as follows. Intense slip deformation is activated in the margin of softer αp and αl, while the neighboring βt is relatively hard to deform. Dislocations pile up at grain boundaries and some of them are absorbed by grain boundaries. The absorbed dislocations will slip along interface under shear stress, which then lead to the boundary sliding and shows the bright white stripe (indicated by yellow arrows in Figure 8). On the other hand, it can be found that the included angles between the αl producing Type 2 strain localization and loading axis all range within 60–90° (Figure 4 and Figure 8). This indicates that Type 2 strain localization presents spatial distribution dependence, which may be mainly related to the lamellar morphology of αl.
Figure 10 shows the typical micro-damage features of tri-modal microstructure after larger tensile deformation. According to the damage feature and location, they can also be classified into two typical types: the micro-voids within αp and αl and the micro-cracks at αpt and αlt boundaries, as indicated in Figure 10. It can be found that the αp and αl grains producing micro-voids all present intense slip deformation, which is right the deformation feature of Type 1 strain localization. This suggests that the formation of micro-voids within αp and αl is closely related to Type 1 strain localization mentioned above. On the other hand, the locations of micro-cracks at αpt and αlt boundaries right correspond to the above Type 2 strain localization, which are formed due to the boundary sliding. Thus, it can be concluded that the strain localization plays decisive roles in the formation and features of micro-damage in the tri-modal microstructure of titanium alloy.
Above, it was found that significant grain-scale strain heterogeneities exist in each constituent (αp, αl, and βt) and whole microstructure of the tri-modal microstructure during tensile deformation. Moreover, two types of strain localization may be formed due to the intense slip deformation and boundary sliding. This will then greatly determine the micro-damage behavior. It was found that the unique lamellar α in the tri-modal microstructure has a great effect on the strain heterogeneity and strain localization. As mentioned in Section 2.1, the most striking feature of the tri-modal microstructure is the existence of αl compared to bimodal microstructures. Thus, the effect of αl on deformation behavior was briefly discussed here. As for the micro-scale strain distribution, the αl presents close average strain but lower STD than αp at lower macro-strain (<4.7%), while the αl presents a much larger average strain and STD than both αp and βt at larger macro-strain (≥4.7%). These suggest that αl plays an important role in the strain heterogeneity of the whole microstructure at larger macro-strain (≥4.7%). As far as the strain localization is concerned, strain localization can be generated at the interior and boundary of αl. The strain localization at αl boundary presents spatial distribution dependence. These strain localization characteristics related to αl play great roles in the micro-damage behavior of the tri-modal microstructure. Thus, it is important to control the content and spatial distribution of αl to optimize the tri-modal microstructure and corresponding mechanical properties. However, it is difficult to thoroughly investigate the effects of morphology, volume fraction, size, crystal orientation, and spatial arrangement of each constituent phase on the strain heterogeneity of the tri-modal microstructure by only the experiment method. It is greatly limited by the difficulties in the microstructure morphology tailor, orientation characterization, strain distribution evaluation, deformation mode analysis, and so on. Thus, further micromechanical modeling investigation considering the real microstructure, crystal orientation, slip and damage behavior of each constituent, properties of grain and phase boundaries should be conducted to deepen the understanding of grain-scale deformation and damage behavior in the tri-modal microstructure in the future.

4. Conclusions

In this paper, the grain-scale strain heterogeneity characteristics, strain localization mechanism and its effect on the micro-damage during tensile deformation of titanium alloy with tri-modal microstructure were experimentally investigated. The following conclusions can be drawn:
(1) The strain probability distribution of the whole tri-modal microstructure obeys a normal distribution during tensile deformation. Significant grain-scale strain heterogeneities exist in each constituent (αp, αl, and βt) and the whole microstructure. In addition, some highly deformed regions form at a higher macro-strain and keep the same positions during further deformation.
(2) At lower macro-strain (<4.7%), αp and αl present bigger average strain than βt and the whole microstructure, while the strain heterogeneity of each constituent is small and has negligible change. The strain heterogeneity of the whole microstructure is mainly determined by αp. At larger macro-strain (≥4.7%), the strain heterogeneity of each constituent increases fast, and the strain heterogeneity of whole microstructure is mainly related to αl.
(3) There are two typical types of strain localization regions produced in the tri-modal microstructure. The first type is within αp and αl, which is caused by the transgranular intense slip deformation and presents crystal orientation dependence. The second type is at the αpt and αlt boundaries, which is related to the boundary sliding caused by strain incompatibility. In addition, the second type related to αl presents spatial distribution dependence, which mainly occurs at the αl presenting the included angles of 60–90° with respect to loading axis. These strain localizations greatly determine the micro-damage behavior, thus producing the corresponding micro-voids within αp and αl and the micro-cracks at αpt and αlt boundaries in tri-modal microstructure after larger deformation.

Author Contributions

Conceptualization, P.G.; Methodology, P.G.; Formal analysis, Y.L.; Investigation, P.G.; Writing—original draft preparation, P.G.; Writing—review and editing, P.G., R.W., Z.L., Y.C. and M.Z.; Supervision, P.G.; Figures, Y.L.; Data analysis, R.W.; Data collection, Z.L. and Y.C.; Literature search, M.Z.

Acknowledgments

The authors gratefully acknowledge the support of the National Natural Science Foundation of China (Nos. 51875467, 51605388), Provincial Natural Science Foundation of Shaanxi (No. 2017JQ5020), the Open Research Fund of State Key Laboratory of High Performance Complex Manufacturing, Central South University, the Fundamental Research Funds for the Central Universities, and the 111 Project (B08040).

Conflicts of Interest

The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

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Figure 1. Initial microstructure of the as-received wrought TA15 alloy.
Figure 1. Initial microstructure of the as-received wrought TA15 alloy.
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Figure 2. Processing schedule for obtaining tri-modal microstructure (a) and the obtained tri-modal microstructure (b).
Figure 2. Processing schedule for obtaining tri-modal microstructure (a) and the obtained tri-modal microstructure (b).
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Figure 3. Schematic of the geometry and micro-grid of the tensile specimen (a) and area of interest (AOI) (b). The unit of dimension of sample is mm.
Figure 3. Schematic of the geometry and micro-grid of the tensile specimen (a) and area of interest (AOI) (b). The unit of dimension of sample is mm.
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Figure 4. Axial strain maps at different tensile macro-strains: (a) 1.45%; (b) 2.77%; (c) 4.7%; (d) 12.75%.
Figure 4. Axial strain maps at different tensile macro-strains: (a) 1.45%; (b) 2.77%; (c) 4.7%; (d) 12.75%.
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Figure 5. Variation of probability distributions of axial strain with tensile macro-strain: (a) 1.45%; (b) 2.77%; (c) 4.7%; (d) 12.75%.
Figure 5. Variation of probability distributions of axial strain with tensile macro-strain: (a) 1.45%; (b) 2.77%; (c) 4.7%; (d) 12.75%.
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Figure 6. Variations of average (a) and standard deviation (b) of strain in the whole microstructure and different constituents.
Figure 6. Variations of average (a) and standard deviation (b) of strain in the whole microstructure and different constituents.
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Figure 7. The typical strain localization regions and corresponding grid change within equiaxed α (a) and within lamellar α (b) at macro-strain of 4.7%.
Figure 7. The typical strain localization regions and corresponding grid change within equiaxed α (a) and within lamellar α (b) at macro-strain of 4.7%.
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Figure 8. The morphology of deformed tri-modal microstructure after tensile deformation (the sample surface was mechanically and electrolytically polished before tensile deformation).
Figure 8. The morphology of deformed tri-modal microstructure after tensile deformation (the sample surface was mechanically and electrolytically polished before tensile deformation).
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Figure 9. The typical strain localization regions and corresponding grid change at the boundary of αpt (a) and the boundary of αlt (b) at macro-strain of 4.7%.
Figure 9. The typical strain localization regions and corresponding grid change at the boundary of αpt (a) and the boundary of αlt (b) at macro-strain of 4.7%.
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Figure 10. The micro-damage features of tri-modal microstructure after larger tensile deformation: (a) micro-voids within αp and αl and micro-crack at αpt boundary; (b) micro-crack at αlt boundary (the sample surface was mechanically and electrolytically polished before tensile deformation).
Figure 10. The micro-damage features of tri-modal microstructure after larger tensile deformation: (a) micro-voids within αp and αl and micro-crack at αpt boundary; (b) micro-crack at αlt boundary (the sample surface was mechanically and electrolytically polished before tensile deformation).
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Gao, P.; Li, Y.; Wu, R.; Lei, Z.; Cai, Y.; Zhan, M. Characterization and Analysis of Strain Heterogeneity at Grain-Scale of Titanium Alloy with Tri-Modal Microstructure during Tensile Deformation. Materials 2018, 11, 2194. https://doi.org/10.3390/ma11112194

AMA Style

Gao P, Li Y, Wu R, Lei Z, Cai Y, Zhan M. Characterization and Analysis of Strain Heterogeneity at Grain-Scale of Titanium Alloy with Tri-Modal Microstructure during Tensile Deformation. Materials. 2018; 11(11):2194. https://doi.org/10.3390/ma11112194

Chicago/Turabian Style

Gao, Pengfei, Yanxi Li, Ronghai Wu, Zhenni Lei, Yang Cai, and Mei Zhan. 2018. "Characterization and Analysis of Strain Heterogeneity at Grain-Scale of Titanium Alloy with Tri-Modal Microstructure during Tensile Deformation" Materials 11, no. 11: 2194. https://doi.org/10.3390/ma11112194

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