**2.3 Type of weld residual stresses**

A literature study and a probabilistic analysis of welding residual stresses distribution were performed by Manai et *al* in [8]. They concluded that the probability of occurrence of TRS at the surface is 0.89, substantially, the probability of occurrence of CRS at the surface equal to 0.11. In addition, Manai et *al*. [8] developed a method that determines the shape of welding residual stresses distribution through the thickness direction by knowing only the magnitude of surface welding residual stresses. It was assumed that

*Residual Stresses Distribution Posterior to Welding and Cutting Processes DOI: http://dx.doi.org/10.5772/intechopen.100610*

the residual stresses in the thickness direction at the weld toe has the shape showed in **Figure 2**. Three parameters were used to define this shape which are the magnitude of the surface residual stresses (*σRSA*), the maximum magnitude of the subsurface residual stresses (*σRSB*), and the depth of the maximum sub-surface residual stresses (*DB*).

As welding residual stresses distribution depend on the material properties and the geometry of the plates (thickness of the welded plate), a normalization of the abovementioned parameters that define residual stresses shape is introduced. The magnitude of the residual stresses (*σRS*) was normalized by the yield strength (*σfy*) of the material, (*<sup>σ</sup>RS <sup>σ</sup>fy* ). The depth of the residual stress(*DB*) was normalized by the plate thickness (*T*), (*DB <sup>T</sup>* ). In the section below, a summary of the residual stresses distributions through the thickness direction at the weld toe is stated.

### *2.3.1 Tensile welding residual stresses at the surface*

Based on the probabilistic analysis in Manai et *al*. [8], in the case where welding introduces TRS at the surface, the following conclusions are extracted (regardless of the material and the thickness of the welded plate):


#### *2.3.2 Compressive welding residual stresses at the surface*

In case where welding inroduces CRS at the surface and independent of the material and the thickness of the welded plate, the following points were concluded in Manai et al [8]:

