Issue 50

L. Romanin et al., Frattura ed Integrità Strutturale, 50 (2019) 251-263; DOI: 10.3221/IGF-ESIS.50.21 252 composition and thermal stresses, is the most important problem to solve since it enormously compromises the low cycle fatigue resistance [1]. For this reason, high power density welding technologies [2–4], with a particular attention to electron-beam welding (EBW), are the most favorite. In fact, they ensure a very narrow fusion zone (FZ) as well as heat- affected zone (HAZ) and a reduction in distortion and residual stresses. In particular, the high vacuum, which characterizes the EBW, avoids material contamination and yields deep penetration. Experimental results carried out on a limited number of nickel-base alloys [4–6], showed that it is possible to obtain sound welds by optimizing the welding speed, pre-heating, beam focus and welding current. Thanks to computer development, it is possible to avoid expensive experimental work and use numerical simulation for predicting the stress evolution during welding [7,8]. A typical keyhole weld is usually accompanied by a distinct ‘nail head’ appearance at the top. The first attempts to model this shape were analytical. Klykow et al. [9] combined a depth source, which describes the keyhole effects and the energy related transfer, and a surface source, representing the plume radiation on the workpiece surface. Both sources had a Gaussian power distribution. Here, it was found that, in laser welding, plasma may be regarded as an independent heat source in the surface, and the laser beam as a volume source resulting in a dagger shape form of the penetration zone. Steen et al. [10] combined the point and line source of Rosenthal [11] to model more effectively a keyhole weld and estimate the power actually absorbed by the weld. The line source represents absorption down the keyhole and the point source represents the plasma radiation from the plume. Bonollo et al. [12] studied the effect of the operative pressure on the weld beads of different materials welded using a CO 2 laser beam. An analytical model of the process was developed using two heat sources that allowed the quantitative evaluation of the power distribution between the keyhole and the plume. Experimental and analytical results were in good agreement. Instead of using two sources, Binda et al. [13] proposed a semi-empirical model of the temperature field in laser welding, based on a modification of the Rosenthal solution. The hypothesis of a constant heat rate along the thickness was replaced by a generic unknown function, to be determined from experimental data. All the analytical models do not consider the variation of the thermal properties with temperature and phase change. Besides, they are not able to predict the thermal and residual stress fields induced by the welding process. For this reason, numerical thermo–mechanical models were developed. In high power density welding technology, a conical source shape with Gaussian power density distribution is often used [7,14]. Though the experimental and numerical results are in sufficient overall agreement, a single source is insufficient to reproduce the correct ‘nail’ shape of the fusion zone and thus the local stress development at the FZ–HAZ interface. Du et al. [15], developed a mathematical model for flow simulation of full penetration laser beam welding of titanium alloy. The model is based on a plane heat source on the top surface and a cylindrical heat source along the z-direction, which take into account the plasma effects and the keyhole absorption. The model, based on the numerical solution of the fluid mechanics equations, gave a good prediction of the FZ shape but was not used for the stress evaluation arising from the welding process. Nickel-base superalloys suffer, above all, from weld-cracking tendency [5]. The idea to correlate weld cracking with the stress–strain evolution during weld cooling was developed by Feng et al. [16]. They considered only transversal and longitudinal stresses as a function of weld cooling. Cracking will be promoted if a weak microstructure and/or a sufficiently high tensile stress exists. However, the model does not consider the correct FZ shape of the bead and the 3D distribution of the stress field. Dye et al. [17] proposed a numerical method for the prediction of the processing conditions that are liable for producing defects during welding such as constitutional liquation, solidification cracking and a centreline grain formation. In particular, solidification cracking is assumed to arise due to the generation of a positive transverse stress at the point behind the heat source where the liquid fraction is still significant. The model was applied to TIG welding of Inconel 718 using a semi-analytical solution for the temperature field and a thermal elasto-plastic analysis in two-dimension, assuming a state of plane stress. In such a way, the real shape of the FZ through the thickness and thus the stress component in z-direction was neglected. For this reason, the model is not suitable for the prediction of microfissures formation along the thickness. It is noted that a lack of knowledge is still present in the specific literature on EBW process applied to alloy systems such as Nickel-base superalloys. Mayor [18] investigated the characteristics of Inconel 718 and 706 joints, though welded by GTAW (gas tungsten-arc welding), finding an excellent weldability and good tensile strength at both room and elevated temperature. The thermal effects of welding operations have been observed to affect the desirable structure of the heat- treatable alloys by producing heat-affected zones with poor stress-rupture properties. The properties are substantially restored to the required level, however, by post-weld heat-treatment involving, in general, solution and ageing treatments at conventional temperatures. In this case, age hardening treatment following welding was found to be more than adequate, without a need for a re-solution treatment. Ferro et al. [19] investigated the electron beam welding of Inconel 706. They found a good agreement between thermal-mechanical analysis and experimental data. The numerical model was