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Three-dimensional visco-plastic flow of metals and the temperature fields in friction stir welding have been modeled based on the previous work on thermomechanical processing of metals. The equations of conservation of mass, momentum, and energy were solved in three dimensions using spatially variable thermophysical properties and non-Newtonian viscosity. The framework for the numerical solution of fluid flow and heat transfer was adapted from decades of previous work in fusion welding. Non-Newtonian viscosity for the metal flow was calculated considering strain rate, temperature, and temperature-dependent material properties. The computed profiles of strain rate and viscosity were examined in light of the existing literature on thermomechanical processing. The heat and mass flow during welding was found to be strongly three-dimensional. Significant asymmetry of heat and mass flow, which increased with welding speed and rotational speed, was observed. Convective transport of heat was an important mechanism of heat transfer near the tool surface. The numerically simulated temperature fields, cooling rates, and the geometry of the thermomechanically affected zone agreed well with independently determined experimental values.

Articles you may be interested inMathematical modeling of heat transfer, fluid flow, and solidification during linear welding with a pulsed laser beam A heat-transfer and fluid-flow-based model to obtain a specific weld geometry using various combinations of welding variables J. Appl. Phys. 98, 044902 (2005); 10.1063/1.2001153 Heat and fluid flow in complex joints during gas metal arc welding-Part II: Application to fillet welding of mild steel J. Appl. Phys. 95, 5220 (2004); 10.1063/1.1699486 Heat and fluid flow in complex joints during gas metal arc welding-Part I: Numerical model of fillet welding J. Appl. Phys. 95, 5210 (2004); 10.1063/1.1699485Modeling of temperature field and solidified surface profile during gas-metal arc fillet weldingThe evolution of temperature and velocity fields during gas tungsten arc spot welding of AISI 1005 steel was studied using a transient numerical model. The calculated geometry of the weld fusion zone and heat affected zone and the weld thermal cycles were in good agreement with the corresponding experimental results. Dimensional analysis was used to understand the importance of heat transfer by conduction and convection at various stages of the evolution of the weld pool and the role of various driving forces for convection in the liquid pool. The calculated cooling rates are found to be almost independent of position between the 1073 and 773 K ͑800 and 500°C) temperature range, but vary significantly at the onset of solidification at different portions of the weld pool. During solidification, the mushy zone grew significantly with time until the pure liquid region vanished. The solidification rate of the mushy zone/solid interface was shown to increase while the temperature gradient in the mushy zone at this interface was shown to decrease as solidification of the weld pool progressed. Tracking these solidification parameters with time shows that the weld pool solidifies with decreasing interface stability, i.e., with a higher tendency to form dendrites towards the center of the weld.

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.

Articles you may be interested inMathematical modeling of heat transfer, fluid flow, and solidification during linear welding with a pulsed laser beam J. Appl. Phys. 100, 034903 (2006); 10.1063/1.2214392 Heat transfer and fluid flow in laser microwelding J. Appl. Phys. 97, 084909 (2005); 10.1063/1.1873032 In situ observations of weld pool solidification using transparent metal-analog systems J. Appl. Phys. 93, 4885 (2003); 10.1063/1.1559934 Modeling of the compressible vapor flow induced in a keyhole during laser weldingComputationally efficient heat transfer models of keyhole mode laser welding ignore fluid flow in the gas, liquid, and the two phase solid-liquid regions. These models cannot be applied to high Peclet number systems where convective heat transfer affects weld pool geometry, cooling rate, and other weld attributes. Here we show that by synthesizing features of an existing model to determine keyhole shape and size with rigorous fluid flow and heat transfer calculations in the liquid and the two phase solid-liquid regions, important features of both high and low Peclet number systems can be satisfactorily simulated. The geometry of the keyhole is calculated by assuming thermal equilibrium at the gas/liquid interface and point by point heat balance at the keyhole wall. The heat transfer outside the vapor cavity is calculated by numerically solving the equations of conservation of mass, momentum, and energy. A vorticity based turbulence model is used to estimate the values of effective viscosity and effective thermal conductivity of the liquid metal in the weld pool. It is shown that the temperature profile and the weld pool shape and size depend strongly on the convective heat transfer for low thermal conductivity alloys like stainless steel. For high thermal conductivity aluminum alloys, on the other hand, convection does not play a significant role in determining the shape and size of the weld pool. The computed solidification parameters indicated that the solidification structure becomes less dendritic and coarser with the decrease in welding velocity. The results demonstrate that a numerically efficient convective heat transfer model of keyhole mode laser welding can significantly improve the current understanding of weld attributes for different materials with widely different thermal properties.

The ground state of the one-dimensional half-filled Penson-Kolb-Hubbard model (with competing single-particle and pair hoppings in the presence of on-site Coulomb repulsion) has been investigated by a real space renormalization group method. The ground state energy, energy gap, local moment and several correlation functions are studied to obtain the phase diagram. The phase diagram consists of a spin density wave (SDW) state, a superconducting (SC) phase and a quasi-metallic phase dominated by short range SC correlations for positive values of the pair hopping amplitude; when this amplitude is negative, the phase diagram contains a near-metallic commensurate charge density wave and an SC phase of pairs with centre-of-mass momentum q= pi apart from an SDW phase.

A dimensionless correlation has been developed based on Buckingham's p-theorem to estimate the peak temperature during friction stir welding (FSW). A relationship is proposed between dimensionless peak temperature and dimensionless heat input. Apart from the estimation of peak temperature, it can also be used for the selection of welding conditions to prevent melting of the workpiece during FSW. The correlation includes thermal properties of the material and the tool, the area of the tool shoulder and the rotational and translation speeds of the tool. The peak temperatures reported in the literature during FSW of various materials and welding conditions were found to be in fair agreement with the proposed correlation.

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