## 1 Introduction  
High-strength aluminum alloys are widely used in aerospace applications due to the high strength-to-weight ratio, good corrosion resistance and high toughness combined with good formability and weldability. High-strength aluminum alloys are broadly employed in aerospace applications owing to the high strength-to-weight ratio, excellent corrosion resistance and great toughness associated with good weldability capabilities and formability. On the other hand, one of the main issues for the contemporary aircraft industry is to ensure simultaneously reliability, high durability, minimum weight and economic efficiency of transport aircraft. To obtain such crafted aircraft characteristics, it is necessary to design structures which ensure high damage tolerance. The approach to engineering design based on the assumption that flaws can exist in any structure and cracks propagate in service, is commonly used in aerospace engineering. Therefore, the prediction of crack growth rates based on the application of fracture mechanics theory is an important aspect of a structural damage tolerant assessment. Many metal components, such as turbines blades, used in aerospace and power industries are subjected to dynamic mechanical loading, leading to the initiation of fatigue cracks. One way to reduce the risk of fatigue crack initiation is to introduce compressive stresses in the region of higher stresses concentration, for example by shot peening. At the industrial level, this is a well-established surface treatment technology, despite generating a meaningful rougher surface and therefore surface defects [1]. Considering that most fatigue cracks initiate at the surface, the conditioning of the surface to resist crack initiation and earlier crack growth is a convenient method to enhance fatigue performance. The indentation of each impact, in shot peening process, produces local plastic deformation given rise to a field of surface compressive stresses. Studies by many researchers have shown a positive shot peening effect [2; 3; 4], resulting from the introduction of residual compressive stresses in the subsurface layers of material. Depending on the peened material, there is an Almen intensity for which the optimum fatigue strength is achieved, corresponding to a certain balance between residual compressive stress field and surface roughness damage. Paris's law, which relates fatigue crack growth rate (\(da/dN\)) and stress intensity range (\(\Delta K\)) is the prime approach adopted for characterizing fatigue crack propagation in engineering structures. Fatigue crack growth of the aluminum alloys in the Paris's law regime is affected by microstructure [5; 6; 7] and by the crack closure induced by plasticity, oxidation and surface roughness, especially near threshold regime. Paris law characterizes the rate of crack advance per cycle: \(da/dN=C\Delta K^{m}\). The rate of crack advance per cycle is related to the stress intensity factor range \(\Delta K\). \(C\) and \(m\) are constants that depend on the material, environment and stress ratio. Crack closure is considered a very good approach to explain the influence of mean stress on the fatigue crack growth rate [6; 8]. [PERSON] and [PERSON] [6] showed that crack growth rates of various aluminum alloys varied by a factor of about 20 for some \(\Delta K\) values, suggesting that the main factor to explain that discrepancies was the crack closure effect and the environment. Fatigue cracks tends to grow into a material region which has experienced large plastic strains due to its location in the crack tip plastic zone. Typically, this material is deformed beyond its elastic domain in the direction normal to the crack flanks. The trace of the plastic deformation produced is left in the crack's path. It acts in the same way to an additional wedge stick between flanks, thus pre-straining them and partly protecting the crack tip from the action of posterior loads.