## 3 Discussion
### Evolution of Slip Systems  
#### 3.3.1 Activation of Slip Systems  
In order to further study the grain interactions of different phases during the plastic deformation, it was necessary to analyze the evolution of slip systems. In this simulation, a total of 155 load steps (macro strain = 15.5%) were carried out to analyze the data of the slip systems, as shown in Figure 8, where the relative frequency meant the ratio of the number of the activated slip systems to the total number activated. In this figure, the relative frequencies showed a tendency of saturation after the macro strain of 2.4%, but their absolute quantity increased, which was similar to the experimental results reported by [PERSON] et al. (2019). On the basis of the data of the \(\alpha\) phase, it is found that the deformation was mainly determined by basal and prismatic slip systems, which was because of the low critical resolved shear stress. With the development of deformation, the pyramidal slip systems activated and the number of pyramidal \(<\)c + a\(>\) slip systems significantly increased. According to the statistics, after reaching the macro strains of 2.4%, 4%, 7.8%, and 15.5%, the relative frequencies of pyramidal \(<\)c + a\(>\) slip systems were 31%, 32%, 32%, and 32%, respectively, which was the highest proportion of the corresponding deformation of the \(\alpha\) phase. By analyzing the slip systems of the \(\beta\) phase, it was found that the slip systems became activated when the step was nine (macro strain = 0  
According to the data in Figure 9, when the macro strain was 15.5%, the prismatic and basal slip systems accounted for 86% and 14%, respectively, of the slip systems with the highest \(\gamma_{s}^{155}\) of each grain in the \(\alpha\) phase. In addition, the \(\gamma_{s}^{155}\) of the \(\left(01\overline{1}\ 0\right)\left[\overline{2}110\right]\) slip system was \(38.97\times 10^{-3}\), which was much higher than others in grain No. 1. This suggested that the \(\left(01\overline{1}0\right)\left[\overline{2}110\right]\) slip system was suitable for slip for grain No. 1. For pyramidal\(<c+a>\) slip systems, they had lower \(\gamma_{s}^{155}\), while the relative frequency in Figure 8 was 32%, which was more than others. In order to determine the leading role of slip systems during the plastic deformation, the relative frequency and \(\gamma_{s}^{155}\) were combined to analyze the contribution of slip systems:  
\[\gamma_{cum}=\sum\gamma_{s}^{155} \tag{18}\]  
where \(\gamma_{cum}\) is the sum of the \(\gamma_{s}^{155}\) of the slip system, \(s\). According to the line chart of Figure 9, the \(\gamma_{cum}\) values of the prismatic slip systems were higher than others, especially the \(\gamma_{cum}\) that was \(40.15\times 10^{-3}\) in grain No. 1, which means the prismatic slip systems play a leading role during the plastic deformation. Furthermore, the highest \(\gamma_{cum}\) of the pyramidal \(<a>\) slip system was \(1.466\times 10^{-3}\) in grain No. 9, which was significantly lower than other  
Figure 8: Activation of slip systems at different macro strains. Figure 9: The (**a**) \(\gamma_{s}^{155}\) and (**b**) \(\gamma_{cum}\) of slip systems of different grains in \(\alpha\) phase at macro strain = 15.5%. slip systems. Meanwhile, it was found that the number of activated slip systems was also less than others. Therefore, the contribution of pyramidal\(<\)a\(>\) to the plastic deformation was the least. When the macro strain was 15.5%, the \(\gamma_{s}^{155}\) and \(\gamma_{cum}\) of the \(\beta\) phase are shown in Figure 10. As we can see, some individual[\(112\)] \(<\)111\(>\) slip systems, such as \((21\overline{1})[1\overline{1}1]\) and \(\left(\overline{1}21\right)\left[\overline{1}11\right]\) in grain No. 2, the \(\gamma_{s}^{155}\) values were \(12.523\times 10^{-3}\) and \(13.271\times 10^{-3}\), respectively, which were significantly higher than others in the same grain.