# Crystal Plasticity Finite Element Modeling on High Temperature Low Cycle Fatigue of Ti2 AlNb Alloy
## 4 Results and Discussion
### Strain and Stress Distribution between the O Phase and b Phase  
For the Ti2 AlNb-based alloy, the crystal system and activated slip systems were different between the O phase and \(\beta\) phase. This will result in an incoordination in deformation process of two phases and may cause stress concentration at the phase boundary. Therefore, in this paper, CPFEM was used to obtain the stress and strain distribution figures of two phases in different cycle stages. The simulation results showed that fatigue reached a stable stage after 10 times cycle deformation, and following studies are based on these results.  
At the 10 th cycle loading, the stress and strain distribution figures of three loading points that 0.7% strain (maximum tension point, point A in Figure 7), 0 strain (zero point, point B in Figure 7) and \(-\)0.7% strain (maximum compression point, point C in Figure 7) were selected, as shown in Figure 9. The Figure 9a,e is stress distribution of \(\pm\)0.7% strain, the points where the stress is significantly higher are highlighted by red circle. All the stress concentration points are located at the phase boundary, and the points at compression stage are greater than the points at the tension stage. Figure 9c shows the stress distribution of B  
Figure 8: Stress–strain curves of experiment, CP simulation and Chaboche model: **(a)** 1.2% strain range; **(b)** 1.3% strain range; **(c)** 1.4% strain range; and **(d)** 1.6% strain range.  
point, even though the strain is 0, the stress at the boundary still reaches up to 300 MPa. Figure 9d,f are the strain distribution of point A, B and C, respectively. There is a large difference between the strain of the O phase and that of the \(\beta\) phase. The strain of the O phase was 0.2-0.8%, the strain of \(\beta\) phase was much greater than 1%, suggesting m the sufficient plastic deformation of the \(\beta\) phase. From the research of [PERSON] [37] and [PERSON] [38], O phase as the hardening phase will lead to dislocation accumulation, and high-density dislocations limit the deformation of the \(\beta\) phase.  
According to the discussion of strain and stress distribution, it was found that phase boundaries are the most important positions relating to stress concentration. Figure 10 shows the rotation angle and stress at 0.7% strain. The rotation angle distribution of each grain is shown in Figure 10a, the stress distribution is shown in Figure 10b. Due to the total strain range at 1.4%, the rotation angles of each grain during fatigue loading are 0.22-0.62\({}^{\circ}\). Although the grain rotation is not significant, the grain rotation angle between the two phases is obviously compared, and the grain rotation has a strong correlation with the stress concentration. The rotation angle is closely related to the phase, and most of the grains with a rotation angle larger than 0.4\({}^{\circ}\) are \(\beta\) phase, and most of them are stress concentration positions, as shown in Figure 10b (circled by solid and dotted lines). The  
Figure 9: Stress and strain distribution figures of three loading points: (**a,b**) 0.7% strain; (**c,d**) 0% strain; (**e,f**) \(-\)0.7% strain. (The O and \(\beta\) phases are also shown in figure, as same as Figure 6a).  
dotted line circles show the position of stress concentration at the grain with large rotation angle, and the solid line circles show the position of no stress concentration at the grain with a large rotation angle. The dotted line circles all are O/\(\beta\) phase boundary, and the solid line circles are all same phase boundary. The plastic deformation ability of the two phases is different; during fatigue loading, \(\beta\) phase is more prone to plastic deformation and grain rotation is more significant. The strain incompatibility between the two phases is more serious, which makes the O/B boundary prone to stress concentration.