3.2 Periodicity of statistical features
Cyclic fatigue involves in plastic deformation caused by dislocation nucleation and movement.43 Fig. 7 shows the statistical results of dislocation density in the model under cyclic loads. Note that only the bcc-Fe matrix is capable of producing identifiable dislocations due to the complex crystal structure of cementite.44 The upper and lower parts of Fig. 7a show the variation of dislocation density with cyclic cycles when d1 is applied along the y -axis and the x -axis, respectively. When the load is along the y -axis, the dislocation density in the first three cycles approaches to zero, corresponding to the elastic deformation process in the first 3 cycles in Fig. 6a. Then the dislocation density increases obviously in the fourth cycle and remains at a high level after that. Note that the increase of dislocation density generally represents the elastic-plastic transition process of the model, which also explains the cyclic softening in Fig. 6a. In addition to that, large amounts of dislocations mean plenty of residual shear strain in the model. When the load is along the x -axis, the dislocation density rises to relatively large values during the first three cycles but falls to close to zero at the end of each cycle (shown in Fig. 7a). This could be corresponding to the nucleation and annihilation process of dislocations in the model. The dislocation annihilation at the end of each cycle might also be the reason why the shear stress peaks in the first three cycles in Fig. 6d hardly change. After the third cycle, the dislocation density stabilizes at a high level due to the dislocation annihilation being hindered, which is also the reason for the cyclic softening in Fig. 6d.
The upper and lower parts of Fig. 7b show the variation of dislocation density with cyclic cycles when d2 is applied along the y -axis and the x -axis, respectively. The dislocation density increases significantly after the first cycle under both loading directions, which is corresponding to the results shown in Fig. 6b and e. High dislocation density after the first cycle led to cyclic softening. The upper and lower parts of Fig. 7c show the variation of dislocation density with cyclic cycles when d3 is applied along the y -axis and thex -axis, respectively. The model is in the plastic stage under d3 as shown in Fig. 5b. The dislocation density has stabilized at a high level since the first stage, which may be the main reason for the yields of shear stress in Fig. 6c and f. Furthermore, the average value of dislocation density increases with the rise of the load and almost has no relation with the direction of the load.