Figure 7 Row of elements (in green) simulating the left side plate A; suppression of the elements of row activation of the symmetric constraints along x direction B.
Also the mechanical properties46,47 have been considered temperature dependent (Figure 6C). Moreover, since the structural analysis involves plastic deformation of the material, in this work, the hardening material model with von Mises yield criterion and the isotropic strain hardening rule have been assumed. The stress vs. strain curves, as a function of the temperature, are shown in Figure 6D.
Moreover, in steels, martensite is formed from austenite containing carbon atoms and, in view of the diffusionless nature of its formation, it ideally inherits the carbon atoms of the parent austenite. Therefore, while for some steel welded parts the solid-state austenite–martensite transformation during cooling has a significant influence on the residual stresses and distortion17,33,34,48,49,50,51, especially when the equivalent carbon content is high, for others (low equivalent carbon content), it may be neglected as well demonstrated by Cho et al52 and Deng.53 According to Cho et al52 and Deng53, the modelling of the transformation phase does not change the level of accuracy of the FE model, in terms of residual stresses and distortions prediction, when the welding process involves low carbon steels with low equivalent carbon content (about Ceq = 0.23%), as the steel used in this work. As a result, the solid-state transformation phase has not been considered in the modelling.
In order to evaluate the influence of the interaction between the plates, a second mechanical analysis has been carried out without considering the row of finite elements placed along the left side of the longitudinal symmetry plane (Figure 7) and by applying only the translational constraints along the x direction to simulate the symmetry constraints.
3. Results and discussion
In this section, numerical results of the welding simulation are presented and compared with experimental ones, in order to assess the reliability of the used FE models.
3.1 Thermal analysis
The temperatures measured at six points by means of six thermocouples have been compared with the respective predicted ones.
Figure 8 shows the temperature distributions at the middle section of the plate along the transverse direction during the two passes, with the welding arc located at the middle of the welding path. It is possible to appreciate a good agreement between numerical and experimental results, with the numerical curves that well estimate the experimental measurements during both welding passes.