**4. Application of the HDM for the analysis of the RS in a welded joint**

As above mentioned, the HMs can be advantageously applied for the RS analysis in welded joints between metal components. As an example, in the following the use of the HDM for the RS analysis on a I type welded joint between two stainless steel plates (AISI 304) is exposed in detail, and the results are compared with that computed numerically by using a FEM procedure accurately accomplished by using accurate thermal analysis of the welding process considered as a progressive process constituted by successive welding passes [18].

**Figure 4** show the geometry of the joint considered and the relative FE model used for the RS analysis, accomplished by considering that the weld bead is formed by 5 successive passes that are simulated by changing the material properties according the temperature profile relieved experimentally by proper thermocouples installed near the weld bead.

The distribution of the RS along the y direction, computed by the numerical simulation process implemented, is reported in **Figure 5**. As expected, it is seen how

#### **Figure 4.**

*Geometry of the welded butt joint considered (a) and relative FE model used for the numerical simulation of the welding process.*

**Figure 5.** *Distribution of the RS along y direction (σy) computed by accurate FE simulations.*

the maximum RS occur at the central zone of the weld bead, with values that fall in the range 200–205 MPa (about 60% the material yield stress).

From **Figure 5** it is seen how the RS vary significantly along the x direction, whereas they vary lightly in the y direction. For this reason the comparison between the RS computed numerically and that estimated experimentally by the HDM is carried out by considering the points 3 and 4 in **Figure 4**, i.e. by considering point near the weld bead in which the geometry of the surface is not significantly modified by the welding process. In detail, the following **Figures 6** and **7** show the comparison between the in-depth RS profile computed by numerical simulations and the RS distribution near the surface computed by using the HDM. The analysis of such figures show how the profile computed numerically is always inside the uncertainty range of the RS computed by means of the HDM, corroborating the accuracy of such an experimental method.
