# Fatigue Crack Growth from Notches:
## 1 Introduction  
In components submitted to cyclic loads, notches act as stress concentrators promoting the occurrence of fatigue failure. An understanding of the effects of notches is therefore fundamental for the proper design of structural components. At a blunt notch, crack nucleation represents the major part of fatigue life, and nominal stress approaches, local stress-strain approaches, critical distance theories, or weighting control parameters-based approaches are used for design [1]. On the other hand, at a sharp notch, the crack nucleates quickly due to the high stresses at the notch root. The propagation phase is dominant, and a fracture mechanics-based approach is usually considered for design. This approach can also be used to predict initiation life, assuming a crack at the notch tip and calculating the number of load cycles required to propagate the crack up to a size detectable by nondestructive inspection methods. In fatigue crack growth (FCG) from notches, there is a confluence of different relevant topics, namely, stress and strain fields at notches, short cracks, and crack closure. There is a great complexity associated with the plasticity induced by the notch, the crack propagation across the stress-strain fields produced by the notch, and the progressive formation of residual plastic wake. Once the crack grows through the notch-influenced region, it may stop growing [2,3]. After the crack exceeds a certain length, the notch geometry has little influence on the FCG of the advancing crack. Different approaches have been followed to study FCG from notches. The stress intensity factor, K, is an elastic parameter with a long dominance in the study of FCG, being also widely used in the case of the notches. [PERSON] et al. [4] predicted fatigue lives in AA2024-T351 by integration of da/dN-\(\Delta\)K laws. Several researchers attempted to modify the K approach to account for the effect of the notch [5; 6; 7]. [PERSON] [8] proposed an effective K model that accounts for notch effects on small cracks by modifying the remotely applied stress term by an appropriate stress concentration factor. However, the FCG rate is usually higher than expected considering da/dN-\(\Delta\)K curves obtained in standard specimens. This odd behaviour was observed in carbon steels [9], stainless steel [10], and aluminum alloys [11]. [PERSON] and [PERSON] [2] proposed that crack closure was the major cause. Generally, this short crack growth effect increases with the decrease of R and the increase of notch severity [12]. [PERSON] and [PERSON] [13] modeled the short crack behavior by considering the stress intensity factors introduced by both the applied load and the residual stresses caused by the notch. [PERSON] et al. [14] introduced a notch-induced magnification factor to modify \(\Delta\)K when the crack was short. [PERSON] et al. [15] introduced an effective \(\Delta\)K to study the short cracks by considering the toughening effect in the phase transformation materials. The plasticity associated with the notch may invalidate the use of linear elastic fracture mechanics [16], and approaches based on nonlinear parameters were exploited. [PERSON] [17] found that the range of the J-integral could account for crack growth in the vicinity of notches. [PERSON] et al. [18] used a finite element analysis to determine the J-integral for the simulation of the crack growth behavior near notches to consider the notch-induced plasticity. [PERSON] and [PERSON] [19] and [PERSON] et al. [20] replaced the range of the J-integral by an effective value with the consideration of crack closure. [PERSON] et al. [21] and [PERSON] and [PERSON] [22] attributed the observed short crack growth phenomenon to the combined effect of the notch plasticity and the crack-tip plasticity. [PERSON] [23] suggested that FCG from a notch was dominated by notch plasticity within the notch plasticity zone and the notch plasticity induced crack closure out of the notch plasticity zone.