# Impact of Cyclic Loading Pattern

The fatigue deformation processes of single crystals and nanocrystalline materials have been explained in detail when a material is simulated under cyclic loading [39].

## Fatigue Crack Propagation of Single-Crystal Nickel during Constant-Strain Amplitude Cyclic Loading

The fatigue crack propagation process of a pre-existing crack in single-crystal nickel by using constant-strain amplitude cyclic loading from MD simulations as per the cohesive zone model is shown in Figure 9.19 [25]. Up to cycle 3, the fatigue

FIGURE 9.19 Fatigue crack growth process of single-crystal Ni during constant-strain amplitude cyclic loading, (a) third cycle tension, *t =* 500 ps, (b) third cycle compression, *t =* 600 ps, (c) fourth cycle tension, *t =* 700 ps, (d) fourth cycle compression, *t* = 800 ps, (e) fifth cycle tension, *t =* 900 ps, (0 fifth cycle compression, *t =* 1000 ps, (g) sixth cycle tension, *t =* 1100 ps, (h) sixth cycle compression, *t —* 1200 ps, (i) seventh cycle tension, *t* = 1300 ps, and (j) seventh cycle compression, *t* = 1400 ps. (From Wu, W.P. et al., *Comp. Mater. Sci.,* 109, 66-75, 2015. With permission.)

crack growth is not obtained because of stress concentration at crack tip. Crack growth initiation occurs at the fourth cycle by dislocations movement near the crack tip, which is clearly observed in Figure 9.19c and d. In the fifth cycle, crack propagation and void generation happen ahead of the crack tip during cyclic loading. Crack propagation (opening and closing) is altered in tension and compression stages of cyclic loading, as illustrated in Figure 9.20. In tension, crack opening is observed, whereas in compression, closing position with voids presents at the crack extension direction. An increase in the loading cycle from cycle 6 to cycle 7 leads to fracture of the specimen by voids amalgamation with crack growth, as displayed in Figure 9.19g—j [25].

FIGURE 9.20 Opening crack in tension and compression stages of (a) cycle 4 and (b) cycle 5 during constant-strain amplitude cyclic loading. (From Wu, W.P. et al., *Comp. Mater. ScL, *109, 66-75, 2015. With permission.)

## Fatigue Crack Propagation of Single-Crystal Nickel during Increasing-Strain Amplitude Cyclic Loading

The fatigue crack propagation process of a pre-existing crack in single-crystal nickel by using increasing-strain amplitude cyclic loading from MD simulations as per the cohesive zone model is shown in Figure 9.21 [25]. The fatigue growth process is not perceived till cycle 3. From cycle 4 onward, the fatigue crack growth process is initiated at the crack tip in stress concentration form. The deformation mechanism behind the crack tip blunting is stress concentration arising at the crack tip. Stress concentration at the crack tip increases proportional to load increment, which leads to the local plastic deformation. Plastic deformation undergoes in the vicinity of crack tip through dislocations generation and persistent slip bands formation. Crack expansion is prevented by relaxing the stress concentration at crack tip with the aid of dislocations and persistent slip bands. In cycle 5, the plastic deformation happens at high-stress regime around the crack tip, as shown in Figure 9.21e and f; this leads to crack propagation along the crack tip direction. In the sixth cycle, the crack growth and crack tip blunting processes are hindered by the generation of dislocations and in addition to persistent slip bands formation around the crack tip [25].

## Fatigue Crack Growth Process of Nanocrystalline Copper during Cyclic Loading

The fatigue crack growth process for nanocrystalline copper containing 5, 20, and 40 grains was illustrated in detail during cyclic loading [40]. Nanocrystalline copper having different grains is modeled by using the Voronoi method [41]. Figure 9.22 shows the fatigue crack growth process of nanocrystalline copper having five grains under cyclic loading. Increasing strain amplitude loading is preferred

FIGURE 9.21 Fatigue crack growth process of single-crystal Ni during increasing-strain amplitude cyclic loading, (a) Third cycle tension, *t =* 400 ps, (b) third cycle compression, *t —* 450 ps, (c) fourth cycle tension, *t* = 550 ps, (d) fourth cycle compression, *t -* 600 ps, (e) fifth cycle tension, *t =* 700 ps, (f) fifth cycle compression, *t* = 750 ps, (g) sixth cycle tension, *t =* 850 ps, and (h) sixth cycle compression, *t =* 900 ps. (From Wu, W.P. et at., *Comp. Mater. Sci.,* 109, 66-75, 2015. With permission.) for nanocrystalline copper with a load ratio *(R* = 0.33). In the figure, part (a) shows the initial position of the pre-existing edge crack. Crack propagation at the crack tip does not take place up to three cycles, but from cycle 4 onward, crack propagation initiates at the crack tip, which is witnessed in part (b). The crack propagation takes place within grain only through persistent slip bands path. The crack propagation reaches to grain boundary from grain in cycle 6, as shown in part (c), owing to the continuous application of cyclic loading. Then, as part (d) illustrates, in cycle 8, the crack propagation occurs along the grain boundary. Finally, part (e) displays the crack propagation, which enters into the alternative grain from the grain boundary. This indicates that the crack propagates across the grain boundary due to the misori- entation of planes being very small between two grains. Fatigue life is proportional to the fatigue crack growth rate.

FIGURE 9.22 Fatigue crack growth process of nanocrystalline copper having five grains during cyclic loading, (a) Initial configuration, (b) fourth cycle, (c) sixth cycle, (d) eighth cycle, and (e) tenth cycle. (From Horstemeyer, M.F. et al., *Int. J. Fatigue*, 32, 1473-1502, 2010. With permission.)

Figure 9.23 shows the fatigue crack growth process of nanocrystalline copper having 20 grains under cyclic loading. The initial configuration in cycle 1 and crack propagation processes in cycle 3 are shown in parts a and b. Crack propagation takes place in cycle 3 on a cleavage mechanism basis. Crack propagation passes through the grain boundary triple junction in cycle 4. There onward, crack propagates along the grain boundary. The grain boundary fails to control the crack growth process of fatigue, which causes to diminish the fatigue life [40].

Figure 9.24 shows the fatigue crack growth process of nanocrystalline copper having 40 grains during cyclic loading. Inside a grain, the fatigue crack

FIGURE 9.23 Fatigue crack growth process of nanocrystalline copper having 20 grains during cyclic loading, (a) Initial configuration, (b) third cycle, (c) fourth cycle, and (d) seventh cycle. (From Horstemeyer, M.F. et al., *Ini. J. Fatigue*, 32, 1473-1502, 2010. With permission.)

propagates through the persistent slip bands. The grain boundary stops the fatigue crack growth with its resistance. The nanocrystalline copper contains grains of 5, 20, and 40, showing dislocations formation under cyclic loading. If the angle between the grain boundary and the crack propagation direction is small, then crack propagates along the grain boundary; otherwise, the grain boundary hinders the crack propagation. Fatigue life is increased by resisting the crack growth. The specimens’ fatigue life depends on the restriction of the crack growth rate, where grain orientations, as well as grain sizes, influence the fatigue crack growth rate [40].

FIGURE 9.24 Fatigue crack growth process of nanocrystalline copper having 40 grains during cyclic loading, (at Initial configuration, (b) fifth cycle, (c) eighth cycle, and (d) tenth cycle. (From Horstemeyer, M.F. et al., *hit. J. Fatigue,* 32, 1473-1502, 2010. With permission.)

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