Modeling and Optimization of Welding Residual Stress

Open Access
Song, Jinseop
Graduate Program:
Mechanical Engineering
Doctor of Philosophy
Document Type:
Date of Defense:
September 22, 2004
Committee Members:
  • Panagiotis Michaleris, Committee Chair
  • Richard C Benson, Committee Member
  • Ashok D Belegundu, Committee Member
  • Tarasankar Debroy, Committee Member
  • Plasticity
  • Finite element
  • Sensitivity
  • Optimization
  • Modeling
  • Residual stress
Modeling and optimization of residual stress in fusion welding and friction stir welding is investigated using nonlinear finite element analysis and direct sensitivity evaluation methods. Fusion welding has been successfully analyzed as a weakly coupled thermal mechanical process (Thermal loads evaluated from the heat transfer analysis are applied to the mechanical analysis) using nonlinear finite element method in Lagrangian frames where the mechanical process is considered thermo-elasto-plastic. Sensitivity formulations are developed using direct differentiation method based on the finite element equations for both thermal and mechanical analysis. These direct sensitivity evaluation algorithms are verified by comparing with the finite difference sensitivity method. Using the gradient optimization algorithm, side heaters are successfully optimized for minimum residual stress in the objective region of the welded structure. Material property sensitivity to residual stress in a fusion welding is also evaluated using the automatic differentiation facility, ADIFOR. An appropriate numerical residual stress prediction algorithm in FSW, which requires a fully-coupled thermal-mechanical analysis because of significant heat generation from large plastic strain dissipation, is not available. Two Eulerian thermo-elasto-plastic formulations are developed as candidate algoorithms to analyze the stress formation in FSW: One is based on the rate equilibrium equation, and the other on the standard equilibrium equation. Each is implemented using a mixed formulationwith Streamline Upwind Petrov-galerkin (SUPG) stabilization for three-dimensional 8-noded brick elements. Strip drawing examples are simulated to investigate the validity and convergence of the two algorithms. A combined thermal-viscoplastic and thermo-elasto-plastic analysis procedure is proposed for steady state analysis and a FSW example is simulated to show the potential of the Eulerian thermo-elasto-plastic algorithms. The main contribution of this thesis is as follows: (a) three-dimensional optimization of thermo-elasto-plastic process, (b) evaluation of material property sensitivity to welding residual stress, (c) Eulerian FE analysis for elastic rate-independent plastic material with equilibrium equation.