**2. Residual stresses in the welded joints**

The main origin of residual stresses resulting from the welding process can be categorized into three factors:


In the case of arc welding, the workpiece is raised to the melting point within a very limited area, but the temperature drops sharply as the distance from the heat source is increased. This is due to:


The above conditions prevent the uniform expansion of the metal and may produce serious internal stresses, distortion and warping. **Figure 1** describes the influence of such a sharp thermal gradient in a simple butt-welded plate.

Types of welding distortion are classified as out-of-plane types (such as buckling, longitudinal bending (bowing), and angular change and in-plane types (such as transverse shrinkage, longitudinal shrinkage and rotational distortion). Several methods for controlling welding distortion are described; some can be applied during welding, and others after welding are completed. As some methods may reduce one distortion mode but increase another, it is imperative to identify the distortion mode of a particular structure before selecting the appropriate distortion mitigation method. Weldinginduced buckling is eliminated by ensuring that the compressive longitudinal residual stress is lower than the critical buckling stress of the plate, either by increasing the critical buckling stress of the plate, reducing the welding residual stress, or modifying the residual stress after welding. Angular distortion is usually controlled by the use of presetting, restraints, or back-side heating. Bowing (also referred to as camber) distortion is controlled by either reducing the welding heat input or balancing the welding residual stress over the cross-section of a structure to minimize the bending moment [1].

Residual stress and distortion affect the fracture behavior of materials by contributing to buckling and brittle fractures at low applied-stress levels. When residual stress and the accompanying distortion are present, buckling may occur at lower compressive loads than would otherwise be predicted. In tension, residual stress may lead to high local

**Figure 1.** *Stresses set up in steel but welded plate (a) on heating (b) on cooling.*

stress in weld regions of low notch toughness. This local stress may initiate brittle cracks that are propagated by any low overall stress that is present. In addition, residual stress may contribute to fatigue or corrosion crack growth and failures [1].

While residual stresses play a major factor in the analysis of fracture response, residual stresses can often be neglected when materials exhibit very high toughness.

The distribution of longitudinal residual stresses can be approximated by the following Equation:

$$\sigma\_{\mathbf{x}}\left(\mathbf{y}\right) = \sigma\_{\mathbf{m}}\left[\mathbf{1} - \left(\mathbf{y}/\mathbf{b}\right)^{2}\right] \mathbf{e}^{-\left(1/2\right)\left(\mathbf{y}/\mathbf{b}\right)^{2}}\tag{1}$$

where,

σ<sup>m</sup> = maximum residual stress which may be as high as the yield stress of weld metal. b = width of the tension zone of σx:

σx; Residual stress in X direction (along the axis of the weld).

σy: Residual stress in Y direction (perpendicular to the axis of the weld).

X: Direction along the weld axis.

Y: Direction perpendicular to the weld axis.
