Residual stresses are self-balanced stress fields found in certain mechanical components in the absence of external loading. Caused by welding, for example, these stresses can potentially affect the behaviour of the structure and its resistance to fracture. When demonstrating the integrity of a mechanical component, particularly in the context of nuclear safety, it is crucial to precisely understand the role of these stress fields on the component's resistance. In the case of fatigue crack propagation, to accurately model all the phenomena involved (stress redistribution, evolution of plasticity, closure effect), it will be necessary to improve numerical tools, such as meshing and crack propagation methods (AMR, X-FEM...) and the J-integral interpolation in the case of through-cracks (Gtheta method). The thesis will consist of two complementary parts: (a) numerical development aimed at improving the Gtheta method in Castem FE code, associated with a 3D crack propagation modelling using AMR, and (b) continuation of component scale tests on fatigue crack propagation in different configurations of residual stress fields.