# Advances in Finite Element Modeling of Fatigue Crack Propagation
## 2 Fundamentals of Finite Element Modeling
### Crack Growth Criteria and Models
The cohesive forces are represented by a traction-separation law, which describes the relationship between the cohesive stresses and the corresponding crack face separations [71; 72; 73]. The CZM results can be sensitive to the finite element mesh size, particularly in the vicinity of the crack tip or cohesive zone, which can lead to mesh-dependent solutions [74; 75]. 5. Continuum Damage Mechanics (CDM) Models: This is another approach used to model crack growth and fracture in materials, which provides a framework for describing the progressive degradation of a material's mechanical properties due to the accumulation of damage, leading to eventual failure. CDM models consider damage as a continuous variable that evolves with the applied loads. The main idea is that the material undergoes microscopic damage accumulation, which leads to macroscopic degradation and ultimately failure. These models aim to capture the complex interaction between material properties, loading conditions, and damage evolution [76; 77]. The main disadvantages of CDM models are the complexity in determining accurate damage parameters [78], the limitations in capturing discontinuous crack growth [79], and the challenges in modeling damage-induced anisotropy [80]. 6. Crack closure models represent a category of fatigue crack growth models that consider the phenomenon of crack closure, where the crack faces make contact during part of the fatigue loading cycle. This interaction can significantly affect the effective stress intensity factor range experienced by the crack tip, subsequently influencing the crack growth rate. By accounting for factors such as plasticity-induced, roughness-induced, and oxide-induced crack closure, these models can provide more accurate predictions of fatigue crack growth rates [81; 82; 83]. Crack closure models can capture the influence of variable amplitude loading, overloads, and underloads on the crack growth behavior, which is important for realistic fatigue life predictions [84]. Whereas accurately modeling the various mechanisms that contribute to crack closure, such as plasticity, roughness, and oxide formation, can be challenging and require extensive experimental characterization [85]. Crack closure measurements were primarily obtained during fatigue crack growth rate tests conducted using load-shedding (K-decreasing) procedures. In contrast, fatigue crack growth in components under service conditions typically experiences K-increasing scenarios, necessitating a multifaceted approach for reconciliation [86]. To address this, models must be calibrated to account for varying closure effects, potentially using an effective \(\Delta\)K that reflects both applied stress intensity and closure impacts. Experimental validation through mixed-mode testing and real-time monitoring techniques can provide additional data, while FEA can help visualize crack behavior under different loading conditions. Establishing empirical relationships between crack growth rates observed in K-decreasing tests and those predicted for K-increasing scenarios will further enhance predictability [87; 88]. 7. Microstructure-Sensitive Models: These models incorporate the effects of microstructural features, such as grain boundaries, inclusions, and precipitates, on fatigue crack growth. Techniques like crystal plasticity finite element methods and multiscale modeling approaches have been used to capture the role of microstructure on crack propagation. These models can provide more accurate predictions of fatigue life by accounting for the effects of grain size, grain orientation, secondary phases, and other microstructural characteristics [89; 90; 91]. Microstructure-sensitive models can provide deeper insights into the underlying mechanisms governing fatigue crack initiation and propagation, such as the role of persistent slip bands, grain boundary effects, and the influence of microstructural heterogeneities [90].