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Three-dimensional (3D) viscoplastic flow and temperature field during friction stir welding (FSW) of 304 austenitic stainless steel were mathematically modelled. The equations of conservation of mass, momentum and energy were solved in three dimensions using spatially variable thermophysical properties using a methodology adapted from well established previous work in fusion welding. Non-Newtonian viscosity for the metal flow was calculated considering strain rate and temperature dependent flow stress. The computed profiles of strain rate and viscosity were examined in light of the existing literature on thermomechanical processing of alloys. The computed results showed significant viscoplastic flow near the tool surface, and convective transport of heat was found to be an important mechanism of heat transfer. The computed temperature and velocity fields demonstrated strongly 3D nature of the transport of heat and mass indicating the need for 3D calculations. The computed temperature profiles agreed well with the corresponding experimentally measured values. The non-Newtonian viscosity for FSW of stainless steel was found to be of the same order of magnitude as that for the FSW of aluminium. Like FSW of aluminium, the viscosity was found to be a strong function of both strain rate and temperature, while strain rate was found to be the most dominant factor. A small region of recirculating plasticised material was found to be present near the tool pin. The size of this region was larger near the shoulder and smaller further away from it. Streamlines around the pin were influenced by the presence of the rotating shoulder, especially at higher elevations. Stream lines indicated that material was transported mainly around the pin in the retreating side.

Heat transfer and visco-plastic flow during friction stir welding of Ti-6Al-4V alloy have been modeled in three dimensions by numerically solving the equations of conservation of mass, momentum and energy using temperature dependent thermo-physical properties and temperature and strain-rate dependent viscosity values. The computed results showed that five important model parameters, i. e., the spatially variable friction coefficient, the spatially variable slip between the tool and the workpiece, the extent of viscous dissipation, the mechanical efficiency and the spatially variable heat transfer rate from the bottom surface of the workpiece significantly affected both the temperature fields and the computed torque on the tool. An important problem in the modeling of friction stir welding is that the values of these five parameters cannot be specified from fundamental principles and, and as a result, computed results are not always accurate. Here we show that by combining the heat transfer and plastic flow model with a genetic algorithm based optimization scheme, the values of the five uncertain parameters can be determined from a limited volume of experimental data so that the model predictions of peak temperatures and cooling rates match well with the experimental results. The computed results show that for the welding conditions reported in this paper, close to sticking condition prevailed at the tool – workpiece interface for all the experiments. The extent of viscous dissipation converted to heat was fairly low indicating lack of intimate atomic mixing in the stir zone. Computed three dimensional pressure distributions and streamlines were consistent with defect-free reliable welds for all conditions of welding studied.

Electron beam welding (EBW) of two important engineering alloys, Ti–6Al–4V and 21Cr–6Ni–9Mn, was studied experimentally and theoretically. The temperatures at several monitoring locations in the specimens were measured as a function of time during welding and the cross-sections of the welds were examined by optical microscopy. The theoretical research involved numerical simulation of heat transfer and fluid flow during EBW. The model output included temperature and velocity fields, fusion zone geometry and temperature versus time results. The numerically computed fusion zone geometry and the temperature versus time plots were compared with the corresponding experimentally determined values for each weld. Both the experimental and the modelling results were compared with the corresponding results for the keyhole mode laser beam welding (LBW).Both experimental and modelling results demonstrate that the fusion zone size in Ti–6Al–4V alloy was larger than that of the 21Cr–6Ni–9Mn stainless steel during both the electron beam and laser welding. Higher boiling point and lower solid state thermal conductivity of Ti–6Al–4V contributed to higher peak temperatures in Ti–6Al–4V welds compared with 21Cr–6Ni–9Mn stainless steel welds. In the EBW of both the alloys, there were significant velocities of liquid metal along the keyhole wall driven by the Marangoni convection. In contrast, during LBW, the velocities along the keyhole wall were negligible. Convective heat transfer was important in the transport of heat in the weld pool during both the laser and the EBW. The computed keyhole wall temperatures during EBW at low pressures were lower than those during the LBW at atmospheric pressure for identical heat input.

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