3.2.2. Detwinning

The deformation slip and twinning mechanisms were enough to define the response of the Mg alloys during simple monotonic loadings. However, in the case of complex loading paths, such as cyclic loadings, this was not the case. One should also define the detwinning mechanisms in these cases, as described in Section 2.3. In-situ Synchrotron X-ray techniques have contributed to investigate the detwinning mechanisms. In the case of Mg and its alloys, Murphy-Leonard et al. [7] incorporated the HEDM technique to investigate the twinning-detwinning in pure Mg. They applied cyclic loading with three different applied strains of 0.4%, 0.52%, and 0.75%. The sample was extruded, and loading was applied along the extrusion direction. The c-axis was mostly perpendicular to the extrusion direction. Accordingly, extension twinning was a favored mechanism during compression loading. To monitor the twin volume, Murphy-Leonard et al. [7] measured the X-Ray diffraction peaks of the basal {0002} planes. In other words, initially, there was no basal {0002} peak intensity along the loading direction. As a twinned child is nucleated and grows, a 86.3◦ reorientation of the basal pole occurs within a parent grain, and the peak intensity starts increasing. Accordingly, Murphy-Leonard et al. [7] introduced the formulation for the twin volume fraction *φ* based on the HEDM data as follows:

$$
\phi = \frac{I\_{LD}}{I\_{ND}^0} \tag{16}
$$

where *ILD* is the basal {0002} peak intensity along the loading direction, and *<sup>I</sup>*0*ND* is the initial basal {0002} peak intensity along the normal direction.

Figure 30 shows the cyclic response of the sample at different loading cycles, including the stress-strain loops, basal {0002} peak intensity along the loading direction, and basal {0002} peak intensity along the normal direction. In cycle 1, Figure 30b shows that the basal {0002} peak intensity along the loading direction remained zero during the tensile part of the loading, which means there no twin nucleation during the initial tensile loading. The basal {0002} peak intensity along the loading direction started increasing at the C-1 point in compression and kept increasing until point B, which was the maximum compression loading. At the same time, at point C-1, Figure 30c shows that the basal {0002} peak intensity along the normal direction started dropping. This was in fact, the reorientation of the c-axis along the normal direction towards the loading direction due to twinning.

As soon as unloading starts, the basal {0002} peak intensity along the loading direction starts decreasing, while the basal {0002} peak intensity along the normal direction starts increasing. In other words, the previously twinned children during compression loading were reoriented back to the parent grains. The twin exhaustion occurred at the point T-2 during the second loading cycle, as shown in Figure 30d–f. The variation of basal {0002} peak intensity in the second cycle followed the same trend similar to the first cycle. However, the twinning initiates at smaller compressive strains C-2 compared to C-1 in the first cycle. In both cycles 1 and 2, the twin was fully exhausted in the tensile loading. However, as shown in Figure 30g–i, all the twinned children were not fully detwinned as the minimum twin volume fraction can be observed at the maximum tension strain A. This twin volume content was named residual twins. Murphy-Leonard et al. [7] showed that the residual twins increased by the number of cycles. One can compare the residual twins in loading cycle 500 at maximum tensile strain (point A) to that of loading cycle 200 to observe the increase in the residual twin content as the number of loading cycle increases.

**Figure 30.** The cyclic response of pure Mg samples during the cyclic loading with a strain amplitude of 0.75% along the extrusion direction, including the stress-strain loops and variations of basal {0002} peak intensity along with loading and normal directions during the cyclic loading (**<sup>a</sup>**–**<sup>c</sup>**) Cycle 1 (**d**–**f**) Cycle 2, (**g**–**i**) Cycle 200 (**j**–**l**) Cycle 500 (After Murphy-Leonard et al. [7]).

Murphy-Leonard et al. [7] also investigated the variation of twin initiation stress and detwinning exhaustion stress versus the number of cycles, as shown in Figure 31, in the case of cyclic loadings with the strain amplitude of 0.75% and 0.52%. The results showed that as the number of cycles increased, the magnitude of twinning initiation stress decreased while the magnitude of the twin exhaustion stress increased. They further investigated the results and analyzed the variation of twin intensity at maximum tensile strain, which can be inferred as the twin residuals, versus the number of cycles in the case of cyclic loadings with the strain amplitude of 0.75% and 0.52%, as shown in Figure 32. The results showed that before the loading cycle 100, there was no twinning intensity at maximum tensile strain independent of the strain amplitude, i.e., there were no residual twins. In the cases of loading cycles higher than 100, the residual twin content increased as the number of cycles increased. Furthermore, the residual twin content of samples subjected to the strain amplitude of 0.75% was larger than those subjected to the strain amplitude of 0.52%. In other words, the residual twin content increased by the strain amplitude. An open-source CPFE software PRISMS-Plasticity [103] was later used to capture the cyclic response of the sample, as shown in Figure 33. The results showed that the CPFE simulation can successfully capture the experimental cyclic stress-strain response.

**Figure 31.** The variation of (**a**) twin initiation stress and (**b**) detwinning exhaustion stress versus the number of cycles in the case of cyclic loadings with the strain amplitude of 0.75% and 0.52% (After Murphy-Leonard et al. [7]).

**Figure 32.** The variation of twin intensity at maximum tensile strain versus the number of cycles in the case of cyclic loadings with the strain amplitude of 0.75% and 0.52% (After Murphy-Leonard et al. [7]).

**Figure 33.** The stress-strain response of pure Mg sample during cyclic loading along the extrusion direction: CPFE simulation results for cycle 2 (Δ symbol) are compared versus the experimental results (After Aagesen et al. [108]).
