Basal slip mediated tension twin variant selection in magnesium WE43 alloy

: Tension twinning nucleation and evolution in Mg WE43 alloy over a large sampling area was investigated using a quasi-in-situ EBSD/SEM method during interrupted compression testing. The results showed tension twins with both high and low macroscopic Schmid factor (MSF) were activated under a compressive stress of 100 MPa with a strain rate of 10 -1 s -1 . Basal slip in most grains dominated at this stress, so nucleation of twin variants required little interaction with non-basal slip, which was different from other studies reporting prismatic slip and/or tension twinning were required to activate some low MSF tension twin variants. The geometric compatibility factor (m') was proved to be an important factor to illustrate tension twin variant selection assisted by basal slip. The analysis indicated m' played a critical role over MSF in tension twin variant selection during twin nucleation stage, and final twin variant types were insensitive with increasing stress but they inherited twin variant types determined at twin nucleation stage. Moreover, which specific grain boundary of a grain with hard orientation for basal slip would nucleate which twin variant could be also validated by m' and largely depended on two factors: (a) high value of m' with 1 st or 2 nd rank between the tension twinning of nucleated twin variant and basal slip in adjoining grains; and (b) intensive basal slip activity in the neighbouring grains before twin nucleation.


Introduction
As long as the tension/compression force is not perpendicular/parallel to Mg crystal <0001> axis, the tension twin is easily activated when the grains are positioned in hard orientations for basal slip after deformation due to low critical resolved shear stress (CRSS) [1,2]. There are 6 tension twin variants [3,4] and it would be expected that the variant with high macroscopic Schmid factor (MSF) will be activated once the applied stress reaches the CRSS [5]. However, it is common to see a non-Schmid behaviour of tension twin variant selection (e.g., tension twin variants with low MSF were activated instead of the variant with the highest MSF) [6][7][8][9]. Therefore, MSF is not the only factor to control the twin variant selection meaning other factors need to gain a complete understanding of tension twin nucleation and growth.
Local internal stress introduced during deformation could resolve shear stress on a twin variant with originally low MSF and facilitate its activation. However, the determination of these complex internal stresses is extremely difficult to quantify either by experiment or computation [7,9]. Recently, some mechanisms have been proposed to explain this non-Schmid tension twin variant selection behaviour. Jonas et al. [7,8] reported a local strain accommodation model. The activated twin variants with low MSF required less or no strain accommodation via prismatic slip in an adjacent grain than twin variants with high MSF. The CRSS difference between basal, prismatic and even pyramidal slip can be largely reduced by alloying or increasing working temperature [10,11]. The prismatic slip activity could be enhanced and accommodate the local strain caused by adjacent potential high MSF twin variants. However, considerable low MSF tension twin variants were still observed when AZ31 was deformed at 400 ˚C [12]. Therefore, the retardation of high MSF twin variants in some grains cannot be fully explained by the lack of prismatic slip activities. On the other hand, Shi et al. [9] reported cross-boundary twins with low MSF required the most or more prismatic slip and/or tension twin accommodation. Mu et al. [8] stated the nucleation of secondary contraction and tertiary tension twin variant can be correlated with strain accommodation model, but nucleation of primary tension twin variants was controlled by MSF. Most of these studies only investigated post-mortem samples after deformation. Thus, it was challenging to identify whether twinning occurs before or after slip in the immediate neighbourhood. In addition, if twin growth happened in the investigated samples and both two ends of a twin reached the grain boundary, it was difficult to identify at which grain boundary the twin nucleated at.
Another proposed mechanism is that twin variant selection bears a strong relation with geometrical compatibility factor (m') describing strain transfer or compatibility [6,[13][14][15][16][17][18], as described in the following equation [19]. cos cos Because m' has been extended to explain both slip and twinning [18][19][20][21], is the angle between slip directions and/or twinning shear directions, and is the angle between slip and/or twinning planes normal directions in two adjacent grains.
The activated twin variant normally has a high value of m'. Deformation twin activation can be due to the relaxation of local strain induced by twinning or slip in neighbour grains. For example, slip assisted twins were reported by [14,22]. The m' factor was often used to explain the variant selection of paired or connected tension twins, but recently used to validate the variant selection induced by slip [4,14,16,18,23]. The twin nucleation and the direct evidence of slip-twin and twin-twin interactions along various grain boundaries cannot be investigated dynamically by using post-mortem sample analysis. In addition, most research work was based on investigation of conventional AZ31 or AM30 Mg alloy with a strong texture [4, 7-9, 22, 24], but tension twinning behaviour in another group of rare earth (RE) containing Mg alloys with non-basal texture was not thoroughly investigated [16]. Wang et al. [16] used in-situ observation to investigate tension twin variant selection in binary Mg-RE alloys. They proposed m' was an effective criterion in determining tension twin variant selection especially in grains where twinning was not favoured by the loading stress.
However, this conclusion was not based on a statistical analysis and the selected areas could not be representative of the global textures [16]. Therefore, further systematic studies of this dynamic twin response behaviour in Mg-RE systems needs to be conducted. Moreover, tension twin variant types were insensitive to increasing stress but they were inherited twin variant types determined at twin nucleation stage. These results can enable us to accurately predict the twinning behaviour including not only of variant selection but also nucleation position in Mg alloys.

Material
A commercial WE43 alloy supplied by Magnesium Elektron in as-extruded T5 bar form was used in this work. Several rectangular slabs 5(RD)×5(RD) ×10(ED) mm 3 was cut by electrical discharge machining from the extruded bar (where RD is radial direction, ED is the extrusion direction). Solid solution treatment was carried out in a tube furnace with continuous argon flow at 525 °C for 1 hour, followed by cold water quenching [25].

Sample preparation for quasi-in-situ EBSD of compression test
The heat treated samples were ground and polished using SiC paper, 1 m, 0.25 m oil-based diamond suspension, 40 nm OPS suspension. After EBSD scanning, the sample was compressed up to a compressive stress of 100 MPa using a Zwick/Roell universal testing machine at a strain rate of 10 -1 s -1 along one RD direction. The load was then removed immediately and the sample was quickly transferred using a vacuum container to the SEM chamber for further EBSD scanning of the same area that had been scanned before compression. This cycle of compression and EBSD scanning was repeated on the same sample at compressive stresses of 150 MPa, 250 MPa, and 300 MPa. The detailed slip traces and twin distribution within the same sampling area after each compression test were analysed by using Matlab with MTEX codes [26]. Values of the m factor were calculated using in-house codes.
All the EBSD data were collected from the centre of surface plane RD-ED in this study. All Euler EBSD images were used in this work because commonly used Inverse Pole system were all the same as presented in Fig. 2 throughout this paper.

Compression curves
Preliminary work showed that the yield strength of this heat-treated WE43 alloy was around 150 MPa. Therefore, the interrupted compression stresses chosen in this study were 100, 150, 250 and 300 MPa in order to fully capture the twin nucleation and subsequent evolution.. Fig. 1 shows the corresponding compression curves interrupted at the four stresses.
It was evident that this sample started to yield around 150 MPa with a strain rate of 10 -1 s -1 and so 100 MPa was prior to yielding and all other stresses were post-yield.
3.2 Initial microstructure  [4,7,9,14,22,24]. This micro-texture determined by EBSD was very similar to the micro-texture of other samples from different parts of the same bulk sample, as shown in Fig. 3. It should be noted that although the EBSD mapped area in Fig. 3(b) was nearly four times larger than Fig.   2(a), their micro-textures were nearly the same, in terms of texture intensity and texture component distribution. Therefore, this micro-texture of sample used for quasi-in-situ EBSD/SEM in Fig. 2 was representative of the global texture of the large bulk sample.  mode, there are 6 twinning variants that can be activated [3,4]. When a twin is activated, the parent grain and twin share one plane which is referred to as the twinning plane. When illustrated on a pole figure, the position of the shared plane is normal to the orientation of the twin trace [28,29]. This method was used to identify which specific twin variant was activated in grains in this study.  To confirm this, the m' factor was used to correlate with twin variant nucleation and slip. m' was calculated between basal slip of each neighbouring grain and 6 potential tension twin variants of grain 1, unless the neighbouring grain shows other deformation activities other than basal slip (e.g., tension twin occurred in grain 1-2), as listed in Table 1. The MSF is also given for each tension twin variant in Grain 1. It was observed that the specific tension twin variant preferred to be nucleated at grain boundaries with higher m' and intensive basal slip activity (e.g., grain boundaries between grains 1 and 1-1, and between grains 1 and 1-5).

Twin nucleation and growth
It should be noted one of the twin-twin m' values between grain 1-2 and grain 1 was as high as 0.884, so the corresponding twin variant would be nucleated once the local stress increased.
Tracking the same area after further compression to 250 MPa, a tension twin variant with the highest m' was nucleated and marked by a red arrow in Fig. 6(h), which was consistent with the reported twin-assisted arguments [4,22]. Although m' between grain 1-6 and grain 1 was 0.741 and basal slip MSF of grain 1-6 was 0.37, basal slip activity was not intensive at the grain boundary. This may be attributed to the kink produced in front of the slip traces due to local shear. Since there was no basal slip activity and twinning activity in grain 1-4, no transmission activity needed to be considered. Additionally, two sets of prismatic slip activities were induced by the tension twin and basal slip in grains 1-2 and 1-3 when the applied stress was 250 MPa.
Tracking the same area after further compression to 300 MPa, it was evident that the twin grew with the increased stress. The new twins produced at higher stress had the same variant type as the pre-existing twins formed at the lower stress, with no new tension twin variants produced. to the local stress of the kink caused by pyramidal slip, and this is not the main focus of this paper but will be discussed in another paper. However, a small part of the former twin variant was correctly indexed in Fig. 8(c). This became clearer in Fig. 8(d) with stress up to 250 MPa.
3.3.3 Tension twin variant with a small macroscopic Schmid factor activated favourably in a grain Fig. 9(a) shows the region of interest 3 in Fig. 2(a) after being compressed to a stress of 100 MPa. Fig. 9(a) gives the EBSD all Euler map which only shows traces of one twin variant, although three twin variants can be identified in the corresponding SEM image ( Fig.   9(b)). The EBSD failed to index all twins because of their small size. Fig. 9(c) clearly identified each twin variant position and matched well with the twinning plane traces in Fig.   9(a-b). Surprisingly, the twin variant with the 4 th highest m was preferentially nucleated at the grain boundary. Table 3   MPa. When the stress was increased to 150 MPa, the basal slip was activated in grain 3-5 and tension twin occurred subsequently in grain 3 (red arrow shown in Fig. 10(a)). With increasing stress to 250 MPa, more twins were stimulated by basal slip, but again no new twin variant was nucleated. Fig. 11(a) gives the region of interest 4 in Fig. 2(a) after being compressed to a stress of 100 MPa. In Fig. 11(b), the EBSD All Euler map only shows one twin variant due to indexing problems associated with the small twin size. However, the SEM image shown in

MSF(m)-m' ranks
To obtain a statistical result, all the nucleated tension twins in the entire big sampling area after being compressed at 100 and 250 MPa in Fig. 2 were analysed by the same way as illustrated in sections 3.1-3.4. Fig. 12 (a-c) shows some tension twins were activated around kink bands, bugling grain boundaries or were isolated in the grain interior without connecting any grain boundaries (marked by red arrows in Fig. 12). These twinned grains (about 2% of total twinned grains) were excluded for statistical analysis of MSF(m)-m' ranks, since they were more likely to be caused by local stress fluctuation and/or strain transmission from the grains below the sapmpling area surface. After ignoring these small amount of twinned grains, the number of other tension twins, nulceated at grain boundaries in 47 grains, was 237 after sample being compressed at the stress of 100 MPa. At the stress of 250 MPa, the number of twinned grains was 55 with 345 tension twins. These tension twins were considered for statistical analysis below. Therefore, there was no significant difference in tension twinning behaviour from 100 MPa to 250 MPa, which indicated that twin variant activation was determined at low stress, only 100 MPa in this case. Further increasing compressive stress mainly influenced and assisted twin growth. With increasing stress, non-basal slip activities including prismatic and pyramidal slip systems were increased. However, after careful examination of the entire sampling area, no new twin was directly linked or produced around non-basal slip areas.

The effect of de-twinning behaviour on twinning behaviour during interrupted compression test
De-twinning occurs significantly when the external force is reversely loaded in Mg alloys [11,30,31]. However, de-twinning only slightly happened if only unloading the original force [30]. In this study, the compression test was interrupted at the stress of 100, 150, 250 and 300 MPa. Fig. 13 Fig. 14 presents a typical de-twinning region. In Fig. 14(a), weak basal slip traces (marked by blue line) of the right grain can be observed due to low MSF of basal slip (Fig. 14(c)) and several tension twins were produced after being compressed at 100 MPa. In contrast, the basal slip traces of the activated twins (marked by green line in Fig. 14(b)) were quite evident because of high MSF of basal slip. It was not difficult to observe that some of the basal slip traces were out of twinning boundaries (marked by red arrows). This was caused by de-twinning or twinning shrink when the external compressive force of 100 MPa was unloaded. When the compressive stress was increased and unloaded at 250 MPa, this de-twinning behaviour was more obvious (Fig. 14(b)). However, this de-twinning behaviour did not affect the twining variant selection: activated twins were only shrunk but not disappeared, and the tension twin variant selection behaviour was quite similar at the stress of 100 and 250 MPa (Fig. 13).
Therefore, the effect of de-twinning on tension twin variant selection could be ignored in this study. Certainly, the neighbouring grains above and below the centred grains in all the sampling area were not considered in this work, but a research of 3D analysis of tension twin variant selection is now ongoing.

Discussion
It is also found the final twin variant types were mostly determined at the very early stage of compression. The subsequent increased stress further increased the twin number and facilitate the twin growth. Increasing stress did not change the tension twinning variant selaction behaviour considerably. This was confirmed by statistical analysis of slip trace in each grain by using the combination of SEM and EBSD (e.g., Figs. [4][5][6][7][8][9][10][11] and the results were summarised in Fig. 13. The tension twin variants with higher MSF had a growth advantage over the tension twin variants with lower SF within the same deformed grain, which was consistent with the results concluded in [6], but more systematic work will be needed to thoroughly investigate this. During twin growth, some twins grew across the grain to reach the opposite grain boundary. Whether these twins could be transmitted into the neighbouring grains or were constrained inside the twinned parent grains was correlated with m'. For example, the twin assisted twin variants shown in Fig. 6(h) and Fig. 11 (1) Tension twins with both high and low MSF can be activated under the compressive stress of 100 MPa before reaching CRSS of tension twinning in WE43. Therefore, tension twin variant selection, even twin variants with high MSF, was not controlled by MSF, which was opposite to the conclusion in ref. [8].
(2) Basal slip dominated at the stress of 100 MPa, so the twin variant nucleation required no or significantly less interaction with non-basal slip, especially prismatic slip. This was different with the conclusions listed in ref. [9,32] reporting prismatic slip was required to activate one group of low MSF tension twin variants.
The insets are the corresponding (0002) pole figures.     Fig. 9(b-c) f activated twining variant yellow highlighted in Fig. 9(b-c) g activated twining variant green highlighted in Fig. 9(b-c) in Grain 4 tabulated with the MSF for each twin variant  Fig. 11(b-c)