# Advances in Finite Element Modeling of Fatigue Crack Propagation
## 2 Fundamentals of Finite Element Modeling
### Material Modeling for Fatigue Crack Growth
Unlike traditional models that focus solely on stress and strain, CZMs incorporate the material's resistance to crack opening, allowing for a more detailed representation of the crack propagation process. This approach is particularly valuable in capturing the complex interactions between cracks and the surrounding material [49; 50; 51]. Recently, an adaptive phase field framework for the simulation of crack nucleation and propagation in brittle materials for modeling anisotropic brittle fracture was developed by [52; 53; 54]. The mechanism of fatigue damage is inherently cycle-dependent. Time-dependence in fatigue crack growth is intricately related to time-dependent deformation processes, such as creep, as well as environmental factors like oxidation and corrosion. These influences necessitate modifications to finite element models to accurately account for their effects on crack growth behavior. Creep-fatigue interaction models analyze how materials react to cyclic loading while considering time-dependent deformation processes such as creep. This includes the nucleation and propagation of surface and subsurface cracks, which coalesce with internally distributed damage, such as creep voids and cavities [55]. By integrating both creep and fatigue effects through constitutive equations that capture elastic and plastic behavior, these models yield valuable insights into crack growth under various loading conditions, particularly at elevated temperatures [56; 44]. In contrast, corrosion-fatigue models examine the influence of corrosion on crack initiation and propagation. Utilizing modified Paris laws, these models factor in environmental conditions that can accelerate fatigue damage, providing a more accurate understanding of how corrosive environments impact material integrity. This is especially crucial for components subjected to harsh operating conditions [57; 58]. Moreover, oxidation-enhanced crack growth models focus on the effects of oxidation on mechanical properties, particularly how oxide layers affect stress states at crack tips. By addressing the role of oxidation, these finite element models assist in predicting crack growth rates in high-temperature applications where oxidative environments are prevalent [59]. It has long been established that restricted slip reversibility is the primary mechanism behind fatigue crack propagation in metals [60]. Initially, dislocations within the metal's crystalline structure can move and return to their original positions, facilitating reversible slip. However, as loading progresses, irreversible plastic deformation accumulates, particularly around the crack tip, leading to localized dislocation activity and the formation of persistent slip bands (PSBs) [61]. These PSBs serve as initiation points for cracks, and as the crack advances, each load cycle contributes to the formation of fatigue striations on the fracture surface, with their spacing correlating to the crack growth rate. Furthermore, the interaction between the crack tip and microstructural features, such as grain boundaries, significantly affects crack propagation. Therefore, understanding restricted slip reversibility is crucial for accurately predicting the fatigue life and reliability of metallic components.