**3. Effect of residual stresses on fatigue**

Welding residual stresses modify the mean stress experienced by a welded joint under the fatigue loading. In case where high TRS is presented at the welded area, it is assumed that cyclic stresses are fully damaging. Therefore, the effect of welding residual stresses must be taken into account when dealing with welded joints. This effect appears in the calculation of crack growth. As *da dN* (*a* is the crack depth and *N* is the number of cycles) and Δ*Kth* (stress intensity factors range threshold) depend through the stress ratio (*<sup>R</sup>* <sup>¼</sup> *<sup>σ</sup>min <sup>σ</sup>max*, where *σmin* is the minimum stress and *σmax* is the maximum stress) on the mean stress (*σm*). TRS increases the mean stress, therefore accelerates crack propagation. Ultimatly, CRS decreases the mean stress, therefore, leads to the retardation of crack propagation.

In the case where TRS is introdcued at the welded area, crack propagation occurs even when the structure, component, or specimen is subjected to external compressive stress cycles.

In Manai [9], simulations of the fatigue life of as-welded structures in the case of the presence of TRS at the surface and in the case of the presence of CRS at the surface were carried out. It was stated that the fatigue life increases with a factor of 4.5 times in the case of CRS occurred at the surface after the welding process in comparison to the case where TRS occurred at the surface (after welding).
