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

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## Abstract

**:**

_{p}), lamellar α (α

_{l}), and β transformed matrix (β

_{t})) 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 (α

_{p}, α

_{l}, and β

_{t}) and the whole microstructure. At lower macro-strain, α

_{p}and α

_{l}exhibit higher average strain than those of β

_{t}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 α

_{p}. 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 α

_{l}in this deformation stage. On the other hand, two types of strain localization may be generated within α

_{p}and α

_{l}and at the α

_{p}/β

_{t}and α

_{l}/β

_{t}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 α

_{l}. These strain localizations greatly determine the micro-damages, thus forming the corresponding micro-voids within α

_{p}and α

_{l}and the micro-cracks at α

_{p}/β

_{t}and α

_{l}/β

_{t}boundaries in tri-modal microstructure at larger deformation.

## 1. Introduction

_{2}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 (α

_{p}), lamellar α (α

_{l}), and β transformed matrix (β

_{t}). 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.

## 2. Experimental Procedure

#### 2.1. Material and Initial Microstructure

_{p}, 21.6% α

_{l}, and β

_{t}balance. The most striking feature of a tri-modal microstructure is the existence of α

_{l}compared to equiaxed and bimodal microstructures.

#### 2.2. Tensile Testing and Mapping of Strain Field

_{4}+ 65% CH

_{3}OH + 40% C

_{4}H

_{10}O for 40 s firstly. The electron beam lithography technique was then employed to print a gold micro-grid with the area of 1 × 1 mm

^{2}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).

## 3. Results and Discussion

#### 3.1. Characteristics of Strain Heterogeneity

_{p}and α

_{l}and at the α

_{p}/β

_{t}and α

_{l}/β

_{t}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.

_{i}is the amount of points locating in the strain Range i, and N

_{total}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.

_{p}, α

_{l}, and β

_{t}). 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 α

_{p}and α

_{l}are close and slightly larger than WM and β

_{t}, 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 α

_{p}and α

_{l}are softer than β

_{t}at room temperature. Thus, α

_{p}and α

_{l}are easier to deform than β

_{t}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 α

_{p}is much bigger than other constituents, which suggests that α

_{p}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 α

_{l}are both obviously larger than other constituents, which is related to the formation of strain localization regions near α

_{l}(see Figure 4c,d). On the contrary, α

_{p}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 α

_{l}plays a more important role in the strain heterogeneity of WM at larger macro-strain (≥4.7%). It can be concluded that the softer α

_{p}and α

_{l}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

_{p}and α

_{l}; Type 2, strain localization at the α

_{p}/β

_{t}and α

_{l}/β

_{t}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 α

_{p}and α

_{l}, as indicated by the ellipses. Meanwhile, quantities of slip lines are found within some α

_{p}and α

_{l}in the surface of deformed microstructure, as shown in Figure 8. These suggest that the dislocation slip is the main deformation mode within α

_{p}and α

_{l}; 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 α

_{p}and α

_{l}grains. Even for some adjacent grains, only individual grains will produce strain localization. For example, there are two adjacent α

_{p}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 α

_{p}and α

_{l}are strongly dependent on the crystal orientation, which are easier to take place in soft-oriented α

_{p}and α

_{l}. Thus, the neighboring grains may present different degrees of slip deformation and strain localization. These indicate that Type 1 strain localization within α

_{p}and α

_{l}present crystal orientation dependence.

_{p}/β

_{t}and α

_{l}/β

_{t}, which implies the boundary sliding occurs in these regions. Barkia et al. [15] have also observed the boundary sliding at α

_{p}/α

_{p}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 α

_{p}/β

_{t}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 α

_{p}and α

_{l}, while the neighboring β

_{t}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 α

_{l}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 α

_{l}.

_{p}and α

_{l}and the micro-cracks at α

_{p}/β

_{t}and α

_{l}/β

_{t}boundaries, as indicated in Figure 10. It can be found that the α

_{p}and α

_{l}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 α

_{p}and α

_{l}is closely related to Type 1 strain localization mentioned above. On the other hand, the locations of micro-cracks at α

_{p}/β

_{t}and α

_{l}/β

_{t}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.

_{p}, α

_{l}, and β

_{t}) 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 α

_{l}compared to bimodal microstructures. Thus, the effect of α

_{l}on deformation behavior was briefly discussed here. As for the micro-scale strain distribution, the α

_{l}presents close average strain but lower STD than α

_{p}at lower macro-strain (<4.7%), while the α

_{l}presents a much larger average strain and STD than both α

_{p}and β

_{t}at larger macro-strain (≥4.7%). These suggest that α

_{l}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 α

_{l}. The strain localization at α

_{l}boundary presents spatial distribution dependence. These strain localization characteristics related to α

_{l}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 α

_{l}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

_{p}, α

_{l}, and β

_{t}) and the whole microstructure. In addition, some highly deformed regions form at a higher macro-strain and keep the same positions during further deformation.

_{p}and α

_{l}present bigger average strain than β

_{t}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 α

_{p}. 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 α

_{l}.

_{p}and α

_{l}, which is caused by the transgranular intense slip deformation and presents crystal orientation dependence. The second type is at the α

_{p}/β

_{t}and α

_{l}/β

_{t}boundaries, which is related to the boundary sliding caused by strain incompatibility. In addition, the second type related to α

_{l}presents spatial distribution dependence, which mainly occurs at the α

_{l}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 α

_{p}and α

_{l}and the micro-cracks at α

_{p}/β

_{t}and α

_{l}/β

_{t}boundaries in tri-modal microstructure after larger deformation.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Processing schedule for obtaining tri-modal microstructure (

**a**) and the obtained tri-modal microstructure (

**b**).

**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 4.**Axial strain maps at different tensile macro-strains: (

**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%.

**Figure 6.**Variations of average (

**a**) and standard deviation (

**b**) of strain in the whole microstructure and different constituents.

**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 8.**The morphology of deformed tri-modal microstructure after tensile deformation (the sample surface was mechanically and electrolytically polished before tensile deformation).

**Figure 9.**The typical strain localization regions and corresponding grid change at the boundary of α

_{p}/β

_{t}(

**a**) and the boundary of α

_{l}/β

_{t}(

**b**) at macro-strain of 4.7%.

**Figure 10.**The micro-damage features of tri-modal microstructure after larger tensile deformation: (

**a**) micro-voids within α

_{p}and α

_{l}and micro-crack at α

_{p}/β

_{t}boundary; (

**b**) micro-crack at α

_{l}/β

_{t}boundary (the sample surface was mechanically and electrolytically polished before tensile deformation).

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**MDPI and ACS 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*, 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