Fig. 7 Evolution of dislocation density under different cyclic loads. (a), (b) and (c) show the evolutions of dislocation density under d1, d2 and d3, respectively. Shear stress tensor-yz and shear stress tensor-xz represent the results of loading along the y -axis and the x -axis, respectively. Average density-yz and average density-xz represent the average values of dislocation density when loads are applied along the y -axis and the x -axis, respectively. (d) Periodic variation of dislocation density. Red dotted lines indicate the two peaks of dislocation density in each load cycle.
The elasticity of the model promotes dislocation annihilation, while the plasticity of the model promotes the overgrowth of dislocation. Therefore, the evolution of dislocation density is another manifestation of the elastic-plastic properties of the model. In addition to that, the variation of dislocation density is closely related to the cyclicity of applied loads. Fig. 7d shows a detailed description of the upper part of Fig. 7c. The blue curve at the bottom of Fig. 7d shows the variation of cyclic load with cyclic cycles. The red dotted lines indicate the two peaks of dislocation density in each cycle. The variation of dislocation density is highly periodic and corresponds to the leading edges of the load peaks in the blue curve below. When the load goes to zero, the dislocation density appears to be a minimum. And the minimal values within each cycle are greater than zero, which indicates the plastic accumulation in the model. Large amounts of line defects and concomitant point defects in the model will affect the macroscopic plasticity of the material. When the microscopic defects develop into macroscopic cracks or holes with the motion of shear slip bands in the model, the fatigue life of the material will be adversely affected.