# Fatigue Crack Growth from Notches:
## 6 Conclusions  
A numerical approach based on plastic CTOD range, \(\delta_{p}\), was followed to study fatigue crack growth (FCG) from notches. The identification of fundamental mechanisms was made considering notched and unnotched models, with and without contact of crack flanks. Different parameters were studied, namely, notch radius, crack length, and stress state. The main conclusions are:  
* in unnotched cracked specimens, there is an initial transient regime associated with the stabilization of cyclic plastic deformation, which slows down the FCG rate to a minimum. After this minimum,  
Figure 13: Plastic zone size versus notch radius, considering \(\varepsilon^{p}=0\%\) as criterium for the end of the plastic zone (AA6082-T6; contact). (**a**) Plane strain and (**b**) plane stress.  
which defines the end of initial regime, the crack growth increases the strength of crack tip fields, producing a linear increase of \(\delta_{p}\). The slope increases with the reduction of yield stress, and a linear trend was observed between the slope and the level of \(\delta_{p}\). The linear increase of da/dN with \(\Delta a\) is expected to occur in notched samples after the notch affected zone;
* the introduction of contact produced a major effect on \(\delta_{p}\) in unnotched cracks under plane stress conditions. There is a progressive decrease of \(\delta_{p}\) to a minimum value associated with the formation of residual plastic wake. The minimum value of \(\delta_{p}\) defines the end of the transient regime, which is much more extensive than the transient regime associated with the stabilization of cyclic plastic deformation. The effect of crack closure is very limited under plane strain conditions;
* the notches were found to increase the plastic deformation level at the crack tip. The reduction of notch radius increases the notch effect and reduces significantly the notch affected zone. The limit of this zone was reached only for \(r=1\) mm in this numerical study, being about 0.8 mm for the load level studied. The stress state and material do not affect these trends. As the crack propagates ahead of the notch, a linear relation is observed between \(\delta_{p}\) and notch radius;
* the introduction of contact in notched samples attenuates the effect of notch radius and reduces the notch affected zone;
* concerning the stress state, lower values of \(\delta_{p}\) were obtained for plane strain state compared with plane stress state. This could be expected since the stress triaxiality tends to reduce plastic deformation. Additionally, the effect of stress state is greatly linked with crack closure variations.
* Concerning the material, the global trends related to the influence of notch were found to be independent of material parameters. However, there is a significant influence on crack closure phenomenon. Additionally, there is a global trend for the increase of \(\delta_{p}\) with the reduction of yield stress.  
Conceptualization, F.A.; methodology, F.A.; investigation, M.B. and M.C.; data curation, M.B. and M.C.; writing--original draft preparation, M.B. and M.C.; writing--review and editing, R.B. and P.P. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the project no. 028789, financed by the European Regional Development Fund (FEDER), through the Portugal-2020 program (PT2020), under the Regional Operational Program of the Center (CENTRO-01-0145-FEDER-028789) and the Foundation for Science and Technology IP/MCTES through national funds (PIDDAC). This research is also sponsored by FEDER funds through the program COMPETE--Program Operacional Factores de Competitividade--and by national funds through FCT--Fundacao para a Ciencia e a Tecnologia-, under the project UIDB/00285/2020.  
The authors declare no conflict of interest.