PSI - Issue 61

Orhun Bulut et al. / Procedia Structural Integrity 61 (2024) 3–11

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O. Bulut et al. / Structural Integrity Procedia 00 (2024) 000–000

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3.3. Damage evolution under dwell loading conditions

4 dwell cycles consisting of loading, holding and unloading periods are applied to a randomly oriented polycrystal structure with soft-hard-soft grain arrangement as shown in Fig. 4. The FE model is identical to the previous section in terms of element sizes and grain distributions. Each loading, unloading and holding period takes 50 seconds. A traction boundary condition is applied instead of a displacement hold to have a more realistic representation of the dwell fatigue. However, this inhibits the model’s ability to simulate complete failure due to convergence issues. Thus, the evolution of stress and phase field parameter are shown on the prescribed path over the dwell period at lower stress levels that do not nucleate cracks within the applied number of cycles. In addition to that, 4 cycles without the holding period are applied to observe the behavior of the model without the dwell e ff ect.

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Fig. 4. Polycrystal model with embedded hard-soft grain (left). The red line shows the path used to extract data. Stress in the loading direction over the prescribed path (right).

Fig. 4 shows the distribution of stress in the loading direction on the path after the first and fourth dwell period in each cycle and at the end of fourth cycle for the case without dwell period. The stress peaks at the hard-soft grain boundary and also increases over the dwell period. We observe a characteristic feature of dwell fatigue over the course of the four applied cycles, where the stress in soft grains relaxes with increasing stress over the hard grain. This has been shown numerous times in the literature and is named as load shedding or load redistribution where the stress is passed from soft to adjacent hard grains. Moreover, the distribution of stress after 4 cycles with no dwell period is shown with the dashed line. The variation in stress after 4 cycles is observed to be much smaller than the dwell loading case. In Fig. 5, the distribution of the phase field parameter, which represents the accumulated damage, on the path is depicted. The bulk of the damage is taken during the dwell period, while the phase field evolves quite slowly during the loading period. Thus, the governing damage mechanism is the rate dependent behavior during the dwell period and a comparison with an equivalent cyclic loading without a dwell period su ffi ciently confirms this. Computational restrictions could not allow the application of a high enough number of cycles to observe crack nucleation. Neverthe less, a crack initiation life still can be determined by extrapolating the damage accumulation over a large number of cycles. It is important to note that phase field fracture models for fatigue loading normally incorporate an additional degradation to the fracture toughness to simulate damage accumulation per cycle as in Carrara et al. (2020) which is not included in the current work. Regardless, we are able to observe slight evolution of the phase field per cycle possibly due to the complex anisotropic intergranular interactions.

4. Conclusion

A rate dependent crystal plastic model is coupled with the phase field to study crack nucleation and growth for titanium HCP crystals under both static and dwell fatigue loading conditions. The phase field evolves with energy