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.