A NUMERICAL THERMO-MECHANICAL MODEL FOR THE WELDING AND SUBSEQUENT LOADING OF A FABRICATED STRUCTURE

Abstract In this work a numerical model is developed for the welding and subsequent loading of a fabricated structure. The model treats the weld process as a thermo-mechanical problem. A finite element formulation derived from the uncoupled thermal and mechanical energy balances forms the basis of the model. During the development of the thermal model, two significant problems are discussed. One is the material nonlinearity, which manifests itself in the temperature dependence of the thermal properties, and in the fusion problem, where the material phase change is accompanied by a latent heat effect. This latter is modeled by use of a modified specific heat, since the materials of prime concern are alloys which melt over a finite range of temperature, while the former are introduced through periodic re-evaluation of the properties throughout the analysis. The second problem is that of boundary conditions: The deposition of molten bead on the base is modeled by using the intimate contact boundary condition, which is developed into a set of impulse type equations on the finite element model. Since radiation is a dominant cooldown mechanism, this boundary condition is also included. Thus the first part of work develops a non-linear finite element thermal analyzer capable of modeling all of the above effects. This program is then applied to several problems in order to assess its accuracy. During the second part of the work the mechanical model is described. This is an incremental finite element model in which the basic constitutive descriptions are time independent elastic-plastic behavior with temperature dependent properties, and a creep rate formulation for the time dependent behavior. The development is not based on thermodynamic theories but on direct extension of the classical (isothermal) theories. The model includes finite strain effects during isothermal loading, so that it may be used in the modeling of distortion sensitive structure. The integration of the rate equations is discussed with respect to the introduction of a residual load (total equilibrium) correction; it is shown that suc a correction must be introduced very carefully in a completely incremental formulation such as is developed here. Finally the model is compared with simple bead-on-plate weld experiments, performed with high strength steels. It is found that in one case the experimental approximations are well justified by the finite element results, but there is no agreement with the experimentally measured residual stresses. The suggested explanation for the unique stress patterns observed experimentally is shown to have little effect on the finite element stress predictions, so that it is concluded that the finite element model does not include a significant material behavior in this case. In the second example it is shown that the experimental assumptions were not justified by the results of the present model. In both cases the model predicts the usually expected residual stress patterns. Use of a simple creep formulation is shown to give the same order of residual stress reduction as a result of post weld heat treatment as is measured experimentally.