Modeling of the mechanical effects induced by the tungsten inert-gas welding of the IN718 superalloy
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I. INTRODUCTION
OVER the past 20 years or so, much progress has been made in the development of models to describe the mechanical effects that arise during fusion welding operations.[1,2,3] It is often the distortion pattern and the residual-stress field that are of greatest concern. The magnitude of these depends upon the size and shape of the molten zone (e.g., Reference 4) and hence upon the physics of the arc and the fluid flow which occurs in the weld pool. Unfortunately, at this stage, it is not possible to solve all of the relevant equations in one process model,[5] and moreover, many of the relevant materials parameters for the fluid-flow problem are difficult to measure, or else are highly sensitive to the processing parameters and weld-metal composition. For this reason, a good estimate of the shape of the fusion zone is usually required, and, typically, a distributed heat source is used to simulate the passage of the welding arc. The thermal analysis[6,7] appeals to the heat equation, and so the efficiency of heat transfer to the workpiece must be estimated. The thermal field is then sequentially coupled to an elastic-plastic mechanical model. Since it is the equations of continuum mechanics that need to be solved to yield the fields of stress, strain, and displacement, it is most natural to use the finiteelement method for this purpose. An important consideration concerns the frame of reference used for the analysis. Models have been developed (e.g., References 8 and 9) that solve the relevant equations in the Eulerian or heat-source frame. However, the mechanical problem only rarely reduces to a steady-state one, and often it is complex component geometries or the starting and stopping transients that are of interest. For the analysis of these effects it is the Lagrangian frame that is the most appropriate.[10,11] In general, the mechanical model exhibits a D. DYE, Graduate Student, O. HUNZIKER, Research Fellow, S.M. ROBERTS, Rolls-Royce Research Fellow, and R.C. REED, Assistant Director of Research, are with the Department of Materials Science and Metallurgy, University of Cambridge/Rolls-Royce University Technology Centre, Cambridge, CB2 2QZ, United Kingdom. Manuscript submitted July 27, 2000. METALLURGICAL AND MATERIALS TRANSACTIONS A
number of different characteristics: the overall scheme (Lagrangian or Eulerian), the problem dimensionality (threedimensional, shell, or two dimensional plane stress or plane strain), the integration scheme (large or small strain with various solvers), the element formulation (linear or quadratic, reduced or full integration), the discretization of the problem in space and time, and the material properties. The mechanical properties of relevance are the thermal-expansion coefficient, the elastic moduli, the yield strength, and the post-yield hardening coefficient. For most materials, these parameters are strongly dependent upon temperature. Additionally, it may be necessary to consider other effects such as plastic strain recovery, creep, and metallurgical transform
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