PSI - Issue 42

Sarim Waseem et al. / Procedia Structural Integrity 42 (2022) 1692–1699 Waseem et al. / Structural Integrity Procedia 00 (2019) 000–000

1698

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Fig. 4. Crack path obtained from the linear elastic brittle model under monotonic loading (Left); Fatigue model crack path (Center); Graphic recreation of experimental results of Ingra ff ea and Grigoriu (1990) (right).

crack life. The crack enters the hole from right in the experiments whereas it enters from the bottom in the phase field solution. This may attributed to the fact that the last phase of crack growth happens over two cycles in the simulation, implying growth over a very limited number of increments, which is a recurring stability problem with staggered solutions. A clear disparity can be seen in the di ff useness of the two solutions, though their length scale parameters remain consistent. The incrementation could be considered responsible for this, but beyond that, the fatigue solution does not have a uniform fracture toughness over the crack path, growing higher away from the crack and leading to a much less di ff use phase field solution. An interesting observation is the slight divergence in the crack path when the fracture toughness is varied. This is a rather unexpected result and could once more be attributed to the incrementation. A higher fracture toughness leads to more cycles, which further leads to more increments over the crack life, essentially creating a more accurate crack path for the same boundary conditions. This is most likely the source of the divergence, particularly because the last stage of the crack growth took place in very few cycles, translating to far fewer increments, which has been known to cause convergence issues as far as crack paths are concerned. This is an issue that needs to be solved to greatly increase the utility of phase field fatigue models, where simply by scaling the fracture toughness, millions of cycles can be applied through a system where a single cycle in the phase field model could represent cycles of a several orders higher number, creating a computationally reasonable and accurate system of predicting fatigue crack paths and crack life. A fatigue crack growth model simulating crack closure is studied in ABAQUS, employing the phase field method ology. Existing literature on complex crack growth rates is di ffi cult to adapt to the phase field paradigm, mandating a separate approach. The fatigue damage variable is altered to include crack closure e ff ects to more realistically model the fatigue process and this alteration is found capable of e ff ectively produce crack retardation when single cycle over loads are applied. This retardation e ff ect grows more pronounced with greater overload ratios, producing a realistic material response. Furthermore, the fatigue model is found capable of modeling complex crack paths, producing a realistic, accelerating crack growth. This study is also able to highlight in particular the influence of incrementation in the phase field paradigm, where it can actively control the convergent solution of the crack path. Hence a convergence study is essential in both simple static and fatigue models. While the model successfully demonstrates overload e ff ects, it is currently limited to zero-based loading. In future works, this may be expanded to include loading with non-zero minimum loads. Furthermore, a framework to include the e ff ects of compressive underloads, which have been known to greatly mitigate crack retardation e ff ects when directly following overloads, could eventually be developed based on the proposed methodology. The inclusion of crack closure e ff ects to the phase field fatigue paradigm greatly expands the case applicability of this methodology 4. Conclusion