**1. Introduction**

Residual stresses have a significant effect on the fatigue life of structures. Surface tensile residual stresses (TRS) can cause harm to structures, components or specimens. However, surface compressive residual stresses (CRS) can improve the fatigue life of the structures, components or specimens. In most cases, welding introduces TRS at the surface. Few cases reported that CRS can be found at the surface of welded structures, components or specimens.

Rossini et al. [1] define residual stresses as the stresses that remain within the Structure in the case of absence of external load or thermal gradients after manufacture and material processing (refer to **Figure 1**). The equilibrium of the self-balanced stress can be translated to equilibrium in x-direction gives Eq.(1).

$$\int\_{-h/2}^{h/2} \sigma\_{\text{BS}, \text{x}} d\mathbf{y} = \mathbf{0} \tag{1}$$

Where, *h* is the plate thickness and (*σRS*,*<sup>x</sup>*) is the residual stresses in the x-direction.

**Figure 1.** *Schematic presentation of residual stresses distribution.*

An external load applied to a structure, component or specimen will lead to a stress distribution. If the structure (component or specimen) has residual stresses and its behavior is still elastic, the material will respond to the sum of the stress distribution of the external load and the residual stresses. Eq.(2) expresses the relation between stress distribution in the material (*σ*), the externally applied stress (*σEx*) and the residual stresses (*σRS*).

$$
\sigma = \sigma\_{\text{Ex}} + \sigma\_{\text{RS}} \tag{2}
$$

In case where the structure, component or specimen is submitted to external cyclic loading (*σEx*), the residual stresses do not affect the stress amplitude (*σ<sup>a</sup>*,*Ex*), as it is permanently present in the material, therefore, (Eq.(3)). However, it affects the mean stress (*σ<sup>m</sup>*,*Ex*) (refer to Eq.(4))

$$
\sigma\_a = \sigma\_{a, \text{Ex}} \tag{3}
$$

$$
\sigma\_m = \sigma\_{m, \text{Ex}} + \sigma\_{\text{RS}} \tag{4}
$$

There are several sources that introduce residual stresses, such as production process, heat treatment, welding process, post-weld treatments, etc.

Residual stresses can be classified into two scales namely macro and micro residual stress. RS that occur over long distances within the material are characterized as macro RS. In Withers et *al.* [2], mentioned that the origins of macro stress are peening, welding, shot-peening and Tungsten Inert Gas (TIG) dressing. While, RS that exists either between grains or inside a grain due to coherence at interfaces, crystalline defects, and dislocation stress fields (Withers et *al* [2] and Donato et *al.* [3]) is named as micro residual stresses.

The scale of the residual stress, whether it is micro (intergranular) or macro scale, determines the measurement technique. There is no unique technique that is qualified for measuring all the stress types (micro and macro). Within one specimen or

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


#### **Table 1.**

*Techniques of measuring residual stresses.*

component, measurement of residual stresses using two different techniques, give completely different results. Therefore, for reliable results, it is recommended to select a suitable method for each case. Nasri et *al.* [4], reported that the choice of the measurement technique depends on the scale of the RS.

There are many techniques for residual stresses measurements. These techniques can be grouped into three types namely, nondestructive, semi destructive, and destructive. The following bullets enumerate examples of these techniques:


**Table 1** lists the measurements techniques with their corresponding type and residual stress scale that is aimed to measured.

For welding residual stresses, the most used techniques are x-ray diffraction (Monin et *al* [5]) and neutron diffraction (Paddea et *al*. [6]).

In this chapter, Section 2 is meant to determine the mean factors that determine the type of welding residual stresses at the surface and to provide a probabilistic analysis of the shape and type of welding residual stress at the surface. Section 3 gives an overview of the effect of residual stresses on fatigue life and lists the different causes, and reasons for residual stresses relaxation. A re-distribution of welding residual stresses after the cutting process was studied in section 4.
