Towards understanding twinning behavior near fracture surface in magnesium

1. Introduction

Magnesium and its alloys can offer lightweight alternatives to conventional structural metallic materials due to their outstanding properties, such as low density, high special strength and recyclability [1]. However, as a typical metal with hexagonal structure, deformation twins have to be activated and play an important role for magnesium alloys during plastic deformation because of the limited availability of slip systems, especially at room temperature or high strain rate [[2], [3], [4]]. In general, two types of deformation twins usually occur in deformed magnesium alloys, i.e. {10$\bar{1}$2} extension twin and {10$\bar{1}$1} contraction twin, which of them formed largely depends on the relationship between the directions of loading and c-axis of the grains [2,3]. The former one forms when a tension strain is applied along the c-axis of the grain, and the latter one occurs due to the c-axis of the grains subjected to a contraction strain. In addition to these two kinds of twinning modes, {10$\bar{1}$1}-{10$\bar{1}$2} double twin is also frequently observed in deformed magnesium, which is thought to be closely related to the fracture behavior of magnesium [5]. The occurrence of these twins makes magnesium and its alloys exhibit poor formability and remarkably tension-compression yield asymmetry, which in turn influences their design, processing and application. Hence, understanding the characteristic of microstructures associated with deformation twins, such as the twin type, twin-twin interaction, twinning boundaries (TBs) and their evolution during plastic deformation has aroused great interest in experiments and simulations [[6], [7], [8], [9], [10]].

Within the framework of traditional twinning theory, boundaries of deformation twins should coincide with the corresponding twinning plane [11]. This is usually observed in deformed face-centered cubic (FCC) metals, such as copper and aluminum [12,13]. However, recent experiment observations in magnesium and cobalt indicated that boundaries of {10$\bar{1}$2} deformation twin could heavily deviate from the theoretical twinning plane [14]. Further characterizations at atomic scale suggested that {10$\bar{1}$2} TBs actually consist of sequential {10$\bar{1}$2} coherent TBs and basal-prismatic (BP/PB) interfaces, which may be responsible for such deviation matter [15,16]. Especially, the recent work by Sun et al. [16] indicated that the boundaries of {10$\bar{1}$2} twin tip could entirely consist of BP/PB interfaces. By means of molecular dynamics simulation, Wang et al. [17] and Barrett et al. [18] proposed that the occurrence of BP interfaces might be caused by the interaction between matrix dislocations and TBs. They found that when <a> basal dislocations encountered the boundary of {10$\bar{1}$2} twin, twinning dislocations (TDs) and BP/PB interfaces were formed. However, based on the atomistic simulation, Li et al. [19,20] suggested that the formation of BP/PB interfaces should be ascribed to the shuffle process, which dominates the growth of {10$\bar{1}$2} twin, rather than slip-TB interaction. They further pointed out that when a matrix dislocation met TB, this matrix dislocation would be transmuted or absorbed by TB, which of them taking place depended on the relationship between the Burgers vector of this dislocation and the zone axis of twin [21]. During this interactional process, no BP/PB interfaces occurred.

Twin-twin interaction in materials with hexagonal structure has also been studied widely [8,22,23]. Once different twin variants approach each other, twin-twin boundaries (TTBs) occur. Combination of transmission electron microscope (TEM) and atomistic simulation, Sun et al. [24] found that TTBs could consist of a series of interfacial dislocations formed by the reaction of TDs associated with the twin variants. A similar conclusion was also reached by Yu et al. [22]. These TTBs inhibit the migration of TBs, and in turn influence the further macroscopic performance of magnesium alloys, especially during cycle or fatigue formation, in which twinning/detwinning process may take place alternately. For example, Yu et al. [22] experimentally observed that TTBs were usually parallel to the common interface bisecting two twinning planes and strongly hindered the growth of twins. More recently, the work by Sun et al. [25] indicated that the TTBs could also retard the detwinning behavior when loading was reverse, resulting in the enhancement of yield stress of magnesium alloy.

In addition to {10$\bar{1}$2} extension twin, {10$\bar{1}$1} contraction twin was also observed in deformed magnesium alloys, especially in the region near fracture surface [5]. While, compared to the investigations focusing on {10$\bar{1}$2} twin, work dedicated to study {10$\bar{1}$1} twin behavior in magnesium alloys, such as interfacial characteristic and interactional behavior, is very limited [26,27]. Recently, {10$\bar{1}$1} TBs in cobalt were characterized by using high-resolution transmission electron microscope (HRTEM) and consist of sequential {10$\bar{1}$1} coherent TBs and parallel basal-pyramidal (BPy/PyB) planes [26]. Moreover, by means of atomic simulation, A. Ostapovets et al. [27] firstly studied the interfacial structure of {10$\bar{1}$1} twin tip, which is closely correlated to the propagation forward of {10$\bar{1}$1} twin. They found that {10$\bar{1}$1} twin tip was actually composed of consecutively interfacial defects produced by the matrix dislocation decomposition. Besides, similar to {10$\bar{1}$2} twin, twin-twin interaction also takes place once two {10$\bar{1}$1} twin variants approach each other. However, until now, there has been little wok on these two issues in experiment, i.e. the structural feature of {10$\bar{1}$1} twin tip and the interactional behavior of {10$\bar{1}$1} twin variants, especially at atomic scale. Thus, further detailed characterizations from experimental observation are needed for a comprehensive understanding of growth and interaction of {10$\bar{1}$1} twin.

In the present work, {10$\bar{1}$1} twinning behavior in deformed magnesium, with an emphasis on the structural feature of twin tip and interaction between two {10$\bar{1}$1} twin variants shearing the common [11$\bar{2}$0] zone axis, is investigated by a combination of electron back-scatter diffraction (EBSD) and TEM techniques. The results indicate that {10$\bar{1}$1} coherent TBs, BPys and PyBs can stably coexist at the tip of {10$\bar{1}$1} twin. Also, the apparent “crossing” phenomenon is discovered when two {10$\bar{1}$1} twin variants meet each other. Accordingly, the possible mechanisms responsible for the occurrence of such phenomena are proposed and discussed. These findings are also expected to provide an insight into understanding the twinning behavior in hexagonal close-packed (hcp) metals.

2. Experimental procedures

2.1. Initial material and deformation

The material used in the current work was a commercial hot-rolled AZ31 (3 wt% Al-1 wt%Zn) magnesium alloy sheet. As can be seen in Fig. 1(a), the as-received material presents a full recrystallized microstructural feature with an average grain size of ∼30 μm and a strong basal texture, i.e. the c-axis of the most grains nearly parallel to the normal direction (ND) of the sheet. The dog bone shape samples cut from the center of the sheet were tensioned along the rolling direction (RD) at a strain rate of 1 × 10^-3 s^-1 to the point of cracking. The tension curve and dimension of tension sample are shown in Fig. 1(b). No obvious evident yield plateau can be observed, suggesting that the strain at the early stage of was accommodated by dislocation slips rather than deformation twins. More detailed description of the experimental process and as-received material can be found in Ref. [28].

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Fig. 1.   (a) Inverse pole figure showing the initial microstructure of rolled AZ31 plate and (b) stress-strain curve under tension along rolling direction of AZ31 rolled plate. The dimension of the tension sample is inserted. The samples subjected to EBSD examination were cut from the region indicated by the red rectangular box.

2.2. EBSD and TEM examinations

Then, microstructural features of tensioned samples were examined by EBSD technique firstly. All the examined samples with rectangular parallelepiped shape were cut from the areas away from the fracture surface about 1 mm. Before EBSD investigation, the examined surfaces were grounded mechanically and electropolished using commercial AC2 solution. The EBSD investigations were performed using an HKL Channel 5 system equipped in a FEI Nova 400 FEG-SEM. The step size used in all the investigations was 0.8 μm. The indexed rates of Kikuchi patterns of all the EBSD experiments were better than 80 %.

For TEM analysis, the samples were cut from the center of the samples investigated by EBSD, and thinned by grinding and followed by the low temperature ion thinning technique. Subsequently, TEM and HRTEM were performed by JEM-2100 electron microscope with a voltage of 200 kV and a FEI Tecnai F20-G² electron microscope with a voltage of 200 kV, respectively.

3. Results

3.1. Microstructure

It is well known that {10$\bar{1}$1} deformation twin can be readily activated in magnesium when the c-axis of the grain is subjected to a contraction strain [3]. EBSD maps in Fig. 2(a) and (b) present a typical microstructural feature of samples tensioned along RD. In these two images, a large number of twins can be found, including {10$\bar{1}$2}, {10$\bar{1}$1} and {10$\bar{1}$1}-{10$\bar{1}$2} twins, whose boundaries are highlighted by the red, dark blue and light blue lines, respectively. The theoretical angle/axis for these three types of twins are 86.3°/ <11$\bar{2}$0>, 56.2°/ <11$\bar{2}$0> and 38.5°/ <11$\bar{2}$0>, respectively. In these EBSD maps, the tolerance of ±3° deviation from the theoretical misorientation and axis was considered. The other boundaries colored in grey present the regular grain boundaries with high misorientation angles (>15°). Fig. 2(c) exhibits line profiles for the misorientation angle along the direction indicated by the white arrow in Fig. 2(b). Obviously, the point-to-point profile shows that the misorientation angles across the TBs colored in dark blue are approximately equal to 56°, almost consistent with the ideal {10$\bar{1}$1} twin orientation relation, indicating that these twins indeed correspond to {10$\bar{1}$1} twinning mode.

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Fig. 2.   Typical EBSD results of tensioned samples in band contrast (a) and in verse pole figure map (b); Boundaries of {10$\bar{1}$2}, {10$\bar{1}$1} and {10$\bar{1}$1}-{10$\bar{1}$2} twins are colored in red, dark blue and light blue. (c) Line profiles for the misorientation angle along the direction indicated by the white arrow in Fig. 2(b).

3.2. Multiple twins

Fig. 3(a) exhibits a bright-field TEM image showing the feature of microstructure near fracture region. The electron beam is almost along [11$\bar{2}$0] zone axis. Deformation twins marked by T_i (i = 1, 2, 3, 4, 5) can be found here. The outlines of these deformation twins are denoted by the white lines. The corresponding matrix is denoted by M. The selected area electron diffraction (SAED) pattern taken from region 1 is presented in Fig. 3(b). In this image, the 0001 spots of M and T1 are indicated by the black arrows. Accordingly, the (0002) basal planes corresponding to M and T can be determined, as marked by the black lines in Fig. 3. We measured the misorientation between basal planes of T1 and M, and found that the angle was approximately equal to 31°, very close to the theoretical value of {10$\bar{1}$1}-{10$\bar{1}$2} double twin (30.1°) [29]. Such slight deviation may be ascribed to the slip-TB interaction [28]. This indicates that T1 should belong to {10$\bar{1}$1}-{10$\bar{1}$2} double twinning system. Fig. 3(c) shows the electron diffraction pattern stemming from region 2. Here, the 0001 spots of T1 and T2 are also indicated by the black arrows, and the (0002) basal planes belonging to T1 and T2 are marked by the black lines. The acute angle between basal planes of T1 and T2 is measured as ∼31°, suggesting that T2 also satisfies {10$\bar{1}$1}-{10$\bar{1}$2} double twinning orientation relationship. Thus, the occurrence of one double twin (T2) inside another double twin (T1) constitutes a new type twinning system, i.e. {10$\bar{1}$1}-{10$\bar{1}$2}-{10$\bar{1}$1}-{10$\bar{1}$2} quadruple twin. Other such quadruple twins can also be observed with T1, as marked by the white arrows in Fig. 3. In magnesium alloys, double twin generally indicates {10$\bar{1}$2} twin formed inside {10$\bar{1}$1} twin, which has been frequently observed in experiments. Our current results show that after {10$\bar{1}$1}-{10$\bar{1}$2} double twin formed, {10$\bar{1}$1} twin can also be generated within {10$\bar{1}$2} twin. This may be ascribed to that the resultant stress near fracture region causes a contraction strain along the c-axis of {10$\bar{1}$2} twin. Moreover, the local strain incompatibility may also induce the formation of multiple twinning modes. Furthermore, it should be noted that except for double twin, T2 may also belong to the untwinned matrix. While, as can be shown in Fig. 3, the traces of (0002) basal planes of M and T2 are obviously not parallel to each other, this indicates that T2 should correspond to deformation twin, rather than untwinned matrix.

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Fig. 3.   TEM image showing the feature of deformation twins near fracture region of magnesium alloy. The electron beam is nearly parallel to [11$\bar{2}$0] zone axis. The twins are denoted by T_i (i = 1, 2, 3, 4, 5) and the matrix is marked by M. The selected area diffraction patterns taken from the regions 1, 2, 3, 4 and 5 are presented in Fig. 2 (b-f), respectively. Basal stacking faults within the twins are indicated by the black arrows. The outlines of these deformation twins are denoted by the white lines.

Another twin, which is divided into three segments marked by T3, T4 and T5, respectively, can also be seen in Fig. 3(a). The SAED pattern taken from the area 3 is displayed in Fig. 3(d), indicating that T3 corresponds to {10$\bar{1}$1} twinning orientation relationship, as the actual misorientation (56°) between basal planes of T3 and M is almost equal to the theoretical misorientation of {10$\bar{1}$1} twin (56.4°). Fig. 3(e) and (f) exhibits the results of electron diffraction focusing on the areas 4 and 5, respectively. It shows that the misorientation between basal planes of T3 and T4, T4 and M equals to ∼86° and ∼31°, respectively, suggesting that T3 and T4 constitutes a {10$\bar{1}$1}-{10$\bar{1}$2} double twinning system. The formation of this double twin may adopt the way like that after T3 formed, T4 nucleates and grows within T3. But seemingly, the domain of T3 is not twinned entirely by T4. Consequently, T3 is divided into three parts (see Fig. 3(a)). In addition, it should be noted that a high density of basal stacking faults (SFs) marked by the arrows occur within twins. The both ends of these SFs seems to directly connect with TBs, and the width of them can reach as large as 0.3-1 μm. Such basal SFs ware also observed within {10$\bar{1}$2} and {10$\bar{1}$1} primary twins [30,31]. Recently, Li et al. [31] argued that large atomic shuffle during the migration of TB may be responsible for the occurrence of such basal SFs.

3.3. Boundaries of twin tip

The HRTEM micrograph in Fig. 4(a) exhibits a typical morphology of {10$\bar{1}$1} twin tip that formed during tension along RD. The bright-filed TEM at a relatively low magnification is presented in Fig. 4(b), and the corresponding SAED pattern taken from the region near twin tip is inserted at the upper right corner. In Fig. 4(b), two twin variants marked by T6 and T7 can be clearly seen and interact with each other. The matrix is denoted by M. In these two images, the (0002) basal planes in the matrix and twin should be parallel to the electron beam, i.e. edge on, as the electron beam is along the [11$\bar{2}$0] zone axis. In Fig. 4(a), the trace of (0002) basal planes are highlighted by the black lines. Meanwhile, the trace of (10$\bar{1}$1) and (10$\bar{11}$) can also be identified unambiguously, as marked by the black lines. Importantly, it can be clearly seen that the boundaries of {10$\bar{1}$1} twin tip at atomic scale are not straight, but exhibit a faceted structure. The TBs consist of a series of steps marked by the red lines joining straight terraces indicated by the yellow lines. From the orientation relationship, the straight terraces are almost parallel to the theoretical trace of (10$\bar{1}$1) plane and the red steps seem to coincide with (0002)_T|| (10$\bar{11}$) _M basal-pyramidal (BPy) or (10$\bar{11}$) _T||(0002)_M pyramidal-basal (PyB) planes, just analogous to the BP/PB interfaces in the {10$\bar{1}$2} twinning system [16]. Such interfacial structure feature was also found in {10$\bar{1}$3} and {11$\bar{2}$2} twinning systems [32,33]. Now, two interesting characteristics can be identified from Fig. 4: (i) boundaries of {10$\bar{1}$1} twin actually consist of three kinds of interfaces, including BPy, PyB and (10$\bar{1}$1) interfaces; (ii) the twin tip of {10$\bar{1}$1} twin can end up with BPy and PyB interfaces only. Such interfacial features not only influence the morphology of {10$\bar{1}$1} TBs at a relatively low magnification, but also are closely correlated to the twin growth, these two issues will be discussed in more detail below.

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Fig. 4.   (a) HRTEM image showing the morphology of a {10$\bar{1}$1} twin tip in deformed magnesium. (b) The corresponding bright-field TEM image at a relatively low magnification is inserted. The selected area electron diffraction patterns focusing on the twinning boundary highlighted by the red rectangular box are also inserted. The electron beam is nearly along [11$\bar{2}$0] zone axis. The (0002) basal and {10$\bar{1}$1} pyramidal planes of T6and M are marked by the black lines. Three types of facets are presented in Fig. 4(a), including {10$\bar{1}$1} coherent twinning boundaries (TBs) marked by the yellow lines, (0002)_T|| (10$\bar{11}$) _M basal-pyramidal (BPy) and (10$\bar{11}$) _T||(0002)_M pyramidal-basal (PyB) planes highlighted by the red lines.

3.4. Twin-twin interaction

Fig. 5(a) presents a bright-field TEM image showing the interaction between two deformation twins. Here, the twins and matrix are marked by T6, T7, T8 and M, respectively. The electron beam is nearly parallel to [11$\bar{2}$0] zone axis. To view the microstructures caused by interactional incident more clearly, we show lattice fringes at a larger magnification in Fig. 5(b). In Fig. 5(b), the traces of (0002) basal planes belonging to T6, T7, T8 and M are marked by the yellow lines. Accordingly, the values of misorientation angles across the boundaries of T6 and M, T7 and T8, T8 and M can be easily measured as ∼56°, ∼87° and ∼49°, respectively. Here, the misorientation angle is defined as the acute angle between the (0002) basal planes of twins and matrix. These indicate that T6 corresponds to {10$\bar{1}$1} twinning system. It should be noted that the actual misorientation angle of T6 is lower than the theoretical value (∼56°). The recent work by Sun et al. [28] indicated that such change in misorientation angle in {10$\bar{1}$1} twinning system might be caused by the multiple dislocations activated and interfacial defects formed by slip-TB interaction. The misorientation angle across boundary of T7 and T8 is approximately equal to ∼86°, this indicates that T7 should be consistent with {10$\bar{1}$1}-{10$\bar{1}$2} twinning system, namely that one {10$\bar{1}$1} twin (T8) is formed firstly, than a {10$\bar{1}$2} twin (T7) nucleates and grows inside T8. More importantly, it shows in Fig. 5(b) that after interaction, T6 appears to directly thread T7, resulting in the formation of TTBs marked by the black arrowheads. The traces of TTBs are nearly parallel to the boundaries of T6. Meanwhile, the lattices near the TTBs are distorted seriously, indicating the existence of interfacial defects formed by the twin-twin interaction. Also, such distorted lattice near TTBs may be also attributed to the projection of the inclined TTB, as the electron beam can not be strictly parallel to the [11$\bar{2}$0] zone axis.

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Fig. 5.   (a) Bright-field TEM image showing the interaction of two {10$\bar{1}$1} twin variants (T6 and T7). The electron beam is nearly parallel to the [11$\bar{2}$0] zone axis. (b) A higher magnification showing the twin-twin interaction presented in Fig. 5(a). The (0002) basal planes of twins and matrix are marked by the yellow lines. Twin-twin boundary (TTB) is indicated by the black arrowhead.

An HRTEM image shown in Fig. 6 presents another example of interaction between two {10$\bar{1}$1} twin variants sharing a common [11$\bar{2}$0] zone axis. The twins and matrix in this image are denoted by T9, T10 and M. From the orientation relationship, the (0002) basal and {10$\bar{1}$1} pyramidal planes of twins and matrix are identified and marked by the black lines. Furthermore, the fast Fourier transformation patterns taken from the boundaries of T9 and T10 are inserted at the upper left and lower left corners, respectively. This also indicates both T9 and T10 are consistent with {10$\bar{1}$1} twinning system. Notably, the boundaries of {10$\bar{1}$1} twins here also present a faceted structure, which agrees with the observations in Fig. 4. The traces of (10$\bar{1}$1) and (10$\bar{11}$) twinning planes of T9 and T10 are marked by the yellow and light blue lines, respectively. The BPy and PyB interfaces for these two twins are colored in red. The interactional incident takes place when the tips of T9 and T10 meet each other. As a result, TTB marked by the green line is formed. Interestingly, the trace of TTB seems to be parallel to the (10$\bar{1}$1) twinning plane, which also coincides with the observation is Fig. 5. In addition, it should be noted that in this case, the growth of one twin seems to be entirely inhibited by the other. No “crossing” phenomenon occurs here, which significantly differs from the findings in Fig. 5. This will be discussed in more detail in Section 4.2.

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Fig. 6.   HRTEM image showing the interaction between two {10$\bar{1}$1} twin variants. The electron beam is nearly parallel to [11$\bar{2}$0] zone axis. The fast Fourier transformation patterns taken from the boundaries of T9 and T10 are inserted at the upper left and lower left corners, respectively. The (0002) basal and {10$\bar{1}$1} pyramidal planes of the twins and matrix are marked by the black lines. The outlines of T9 and T10 are described by different colors. As can be shown, the boundaries of both T9 and T10 consist of {10$\bar{1}$1} coherent TBs, BPy and PyB interfaces. The twin-twin boundary (TTB) formed by the interaction is denoted by the green line.

4. Discussions

4.1. Deviation and migration of {10$\bar{1}$1} TBs

The TEM and HRTEM findings in Fig. 4, Fig. 5, Fig. 6 reveal that the boundaries of {10$\bar{1}$1} twin in magnesium alloys are not always parallel to the theoretical {10$\bar{1}$1} twinning plane, but present a faceted characteristic. Actually, the {10$\bar{1}$1} TBs consist of sequential {10$\bar{1}$1} coherent TBs and parallel BPy/PyB planes serrations. Interestingly, the existence of BPy or PyB interfaces has also been recently predicted by Barrett et al. [34] in the frame of topological theory of crystallographic defects. They pointed out that {10$\bar{1}$1} coherent TBs, BPy and PyB interfaces could coexist in the {10$\bar{1}$1} twinning system. Specially, BPy and PyB boundaries could even connect with each other [34]. Our current work provides the direct experimental evidence for the BPy and PyB interfaces in magnesium alloys, which agrees with the prediction by Barrett et al. [34] well. In addition, like {10$\bar{1}$2} TBs presented in Refs. [14,35], the actual boundaries of {10$\bar{1}$1} twin also deviates the theoretical twining planes at a relatively low magnification, as indicated in Fig. 4(b). In order to illustrate the possible origin of such deviation phenomenon, a schematic is employed in Fig. 7. As shown in Fig. 7, the {10$\bar{1}$1} coherent TBs and BPy/PyB interfaces are marked by the yellow and red lines, respectively. Thus, the dashed yellow line would present the interfaces observed at a relatively low magnification. The deviation angle, β, can be obtained from the length of BPy/PyB interface and {10$\bar{1}$1} coherent TB using the equation, tanβ=L1sinα/(L1cosα+L2), where L1 and L2 represent the length of {10$\bar{1}$1} coherent TB and BPy/PyB interface, respectively, and α is the angle between {10$\bar{1}$1} coherent TB and BPy/PyB interface. It can be clearly seen that the actual morphology of TB is closely related to the existence of BPy/PyB interfaces, and the deviation angle will be changed with the length change of L1 and L2.

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Fig. 7.   Schematic exhibitting the deviation phenomenon caused by the terrace-step structure of {10$\bar{1}$1} twinning boundary (TB). The {10$\bar{1}$1} coherent TBs and BPy interfaces are colored in yellow and red, respectively. The deviation angle is referred to as β.

Within the framework of traditional twinning theory, the formation of deformation twins involves two stages, i.e. nucleation and growth [11]. The growth is usually mediated by the motion of existing steps, i.e. TDs, on the corresponding twinning planes. According to the crystallographic calculation by Christian et al. [11], the elementary TD for {10$\bar{1}$1} twinning system has a Burgers vector: b_T=$\frac{4γ^{2}-9}{4γ^{2}+3}$ [10$\bar{12}$] (γ=ca). While, based on the atomistic simulations, Wang et al. [36] and Li et al. [6] pointed out that the most possible TDs associated with the migration of {10$\bar{1}$1} TBs have step heights of two or four (10$\bar{1}$1) planes, i.e. 2bT or 4bT. Such TDs were also observed and identified in experiment [37]. Apparently, the heights of these BPy or PyB interfaces observed in Fig. 4, Fig. 5, Fig. 6 are much larger than that of TDs in {10$\bar{1}$1} twinning system. As proposed by Ostapovets et al. [38], these faceted structures may not migrate as a whole. The similar conclusion was also reached by Barrett et al. [34]. In their view, the BPy or PyB boundary may be formed from the pile-up of {10$\bar{1}$1} TDs, and the migration of them takes place by absorption and emission of individual TDs. When a {10$\bar{1}$1} TD gliding on the {10$\bar{1}$1} coherent TB encountered the junction of {10$\bar{1}$1} coherent TB and BPy/PyB interface, it would be absorbed or transformed by this junction. Meanwhile, another TD would be rapidly formed at the other junction, which joins the BPy/PyB interface and another {10$\bar{1}$1} coherent TB, and continued moving on the {10$\bar{1}$1} coherent TB. Accompanying such process, the BPy/PyB interface migrates upward or downward in order to keep a stable height.

4.2. Mechanism for twin-twin interaction

Twin-twin interaction in hcp materials has been studied extensively [22,23,39]. Some recent publications have shown that when two {10$\bar{1}$2} twin variants sharing the common [11$\bar{2}$0] zone axis meet each other, the tip of one twin will be hindered by the boundary of the other twin and cannot enter the interior of the other twin [22,23]. Since the migration mechanism of {10$\bar{1}$2} and {10$\bar{1}$1} TDs is almost the same, i.e. TDs gliding along TBs, it is therefore possible that the tip of one {10$\bar{1}$1} tip will also terminate at the boundary of the other {10$\bar{1}$1} twin when they approach each other. This speculation can agree with our current experimental observation well, as shown in Fig. 6. It can be clearly seen in Fig. 6 that the interaction between the tips of T9 and T10 takes place, forming a TTB colored in green. No “crossing” phenomenon occurs. Fig. 8 presents a schematic showing the possible interaction process of two {10$\bar{1}$1} twin sharing the same [11$\bar{2}$0] zone axis. In Fig. 8(b), the boundaries of T9 and T10 are marked by the orange and light blue lines, respectively. The TDs gliding on the TBs are denoted by the green symbols of “⊥”, and the arrows indicate the moving direction. When two TDs from different twin variants meet each other at the interactional site, an interfacial defect marked by the brown symbol of “⊥” occurs. In this case, the Burgers vector of this interfacial defect is thus equal to the sum of these two {10$\bar{1}$1} TDs. The corresponding TD reaction may be expressed as:

$b^{1}_{ T9}+ b_{T10}^{2}$ ⇒b_TTB (1)

where $b_{T9}^{1}$ and $b_{ T10}^{2}$ are the Burgers vector of TD belonging to T9 and T10 shown in Fig. 8, respectively. And the b_TTB is the Burgers vector of dislocation associated with TTB. Since the T9 and T10 are the co-zone twin variants, $b_{T9}^{1}$ has Burgers vector of λ[$\bar{1}$012] and $b_{ T10}^{2}$ has Burgers vector of λ[10$\bar{1}$2] or λ[$\bar{1}$01$\bar{2}$]. Here, λ=(4k²-9)/(3+4k²), where k=c/a (k = 1.623 for magnesium). Thus, the Eq. (1) would be changed into:

λ[$\bar{1}$012]+λ[10$\bar{1}$2]⇒4λ[0001] (2)

or:

λ[$\bar{1}$012]+λ[$\bar{1}$01$\bar{2}$]⇒2λ[$\bar{1}$010] (3)

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Fig. 8.   Schematic exhibitting the interaction between different two {10$\bar{1}$1} twin variants. Boundaries of T9 and T10 are colored by orange and light blue, respectively. The twinning dislocations (TDs) are presented by the green symbols of “⊥”. The growth of T9 will be impeded as the twin variants approach each other. The twin-twin boundary (TTB) formed is marked by the red line, and the interfacial defects located on it are denoted by the brown symbols of “⊥” .

Then, the Burgers vector of interfacial defect (b_TTB) would be equal to 4λ[0001] or 2λ[$\bar{1}$010]. The pile-up of these interfacial defects leads to the formation of TTB marked by the red line in Fig. 8(b). As proposed by Yu et al. [22], such TTB would strongly hinder the motion of TDs. Consequently, the tip of T9 cannot further advance and ultimately terminates at the interactional site.

However, the twin-twin interaction presented in Fig. 5 shows a significantly different scenario: one twin (T6) seems to directly thread the other twin (T7). According to the above discussion, such phenomenon is impossible. In general, the propagation of twin tip is thought to be attributed to the successive glide of TDs along the TBs. As TDs move, the crystal lattices of initial matrix are reoriented to transform into that of twin. Thus, the twined and matrix areas are separated by TB. Meanwhile, a certain misorientation angle across TB is formed. Based on this point, if T6 directly threads T7, the crystal lattices on both sides of TTB observed in Fig. 5(b) should satisfy {10$\bar{1}$1} twinning orientation relationship. Whereas, when we revisit the microstructure feature caused by interaction, no {10$\bar{1}$1} twinning orientation relationship is found. This indicates that the apparent “crossing” phenomenon in Fig. 5 should not be caused by the direct penetration. For a better understanding the underlying mechanism behind such apparent “crossing” phenomenon, a series of schematics are employed, as shown in Fig. 9.

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Fig. 9.   Schematic showing the interaction between two {10$\bar{1}$1} twin variants, i.e. T11 and T12. Here, the width of T11 is assumed to be much larger than that of T12. When the tip of T11 approaches the boundary of T12, the growth of a part of T11 will be hindered, while, the tip of the rest part of T11 colored in green in Fig. 9(a) may also continue propagating forward. When this section of movable twin tip bypasses T12, it spreads laterally again, and grows around T12, as shown in Fig. 9(b).

Fig. 9 displays the interaction between T11 and T12. Here, the width of T11 is assumed to be much larger than that of T12. Thus, when these two twin variants approach each other, only one section of T11 impinges on T12, as shown in Fig. 9(a). Consequently, the growth of this part of T11 has to halt, as discussed above. Moreover, it should be noted that except for two kinds of possible TD reactions discussed above, another TD reaction, namely that the TDs of the section of impinging T11 may be direct transformed into interfacial defect residing at the interactional site, may also take place here, since the width of T11 is much larger than that of T12. The corresponding process may be expressed as:

$b_{T11}^{1}$ ⇒ b_TTB (4)

where $b_{T11}^{1}$ and b_TTB are Burgers vector of T11 and interfacial defect located on TTB. In this case, the TTB plane coincides with the twinning plane of T12 and contains interfacial defects that possess the same character as TD associated with the incoming twin T11. While, the tip of the rest part of T11 colored in green in Fig. 9(a) may also continue propagating forward. Therefore, when the section of movable twin tip bypasses T12, it may spread laterally again, and grows around T12, as presented in Fig. 9(b). If so, when a cross-sectional view is made, it just looks likes that T11 directly threads T12. This may well interpret the occurrence of apparent “crossing” phenomenon observed in Fig. 5. In addition, as shown in Fig. 5, overall, the TTB formed accompanying such surrounding process is nearly parallel to the original boundary of T6. This is also consistent with the illustration in Fig. 9 and discussion above. But locally, the TTB in Fig. 5 is distorted seriously, as marked by the white arrowhead. Presumably, such a distorted interface may be closely related to the highly heterogeneous strain caused by the twin collision.

Finally, in the current work, the experimental observations indicate the interaction between different {10$\bar{1}$1} twin variants extensively exist in deformed magnesium. Naturally, such interaction may also influence the macroscopic performance of magnesium and its alloys, especially during cycle loading. Also, the evolution mechanism of TTB caused by {10$\bar{1}$1} twin-twin interaction at atomic scale remains unclear. Then, further studies are needed to focus on these issues.

5. Conclusions

The {10$\bar{1}$1} twinning behaviors in deformed magnesium, with an emphasis on the interfacial structure of twin tip and the interaction between different twin variants sharing a common [11$\bar{2}$0] zone axis, have been investigated by using EBSD and TEM techniques. The main conclusions can be drawn as follows:

(1) A large number of deformation twins can occur near the fracture region in magnesium, including {10$\bar{1}$2} and {10$\bar{1}$1} primary twins, {10$\bar{1}$1}-{10$\bar{1}$2} double twin and {10$\bar{1}$1}-{10$\bar{1}$2}-{10$\bar{1}$1}-{10$\bar{1}$2} quadruple twin.

(2) The HRTEM observations indicate that three kinds of facets, including {10$\bar{1}$1} coherent TBs, BPy and PyB interfaces, can coexist in the {10$\bar{1}$1} twinning system. The twin tip can even end up with BPy and PyB interfaces only. The existence of BPy and PyB interfaces should be responsible for the deviation of actual trace of {10$\bar{1}$1} twin boundary from theoretical {10$\bar{1}$1} twinning plane.

(3) The microstructure characteristic associated with {10$\bar{1}$1} twin-twin interaction is captured. When two {10$\bar{1}$1} twin variants approach each other, the growth of one twin terminates at the boundary of the other twin. The corresponding TTB is nearly parallel to the original boundary of {10$\bar{1}$1} twin. Apparent “crossing” phenomenon observed in experiment may occur as a consequence of one twin surrounded by the other twin.

Acknowledgements

This work was supported financially by National Natural Science Foundation of China (Nos. 51801165 and 51575459), and the Natural Science Foundation of Shandong Province (No. ZR2018BEM001), the Sichuan Science and Technology Program (No. 2019YFH0046), and the Basic and Advanced Research Project of CQ CSTC (No. cstc2017jcyjAX0381).