EXPERIMENTAL AND FINITE-ELEMENT SIMULATION METHODS FOR RATE-DEPENDENT METAL-FORMING PROCESSES

An experimental procedure and a finite element simulation method for rate-dependent metal forming processes are developed. The development includes the formulation of a tangential stiffness matrix for an axisymmetric solid finite element with four node, eight degree of freedom, quadrilateral cross-section. The formulation includes the effects of elasticity, viscoplasticity, temperature, strain rate and large strains. The solution procedure is based on a Newton-Raphson incremental-iterative method which solves the nonlinear equilibrium equations and gives temperatures and incremental stresses and strains. Three examples are studied. In example 1, finite element simulation for the upsetting of a cylindrical workpiece between two perfectly rough dies is performed and the results are compared with alternative finite element solutions. In examples 2 and 3, both experimental and finite element studies are performed for the upsetting of a cylindrical billet and the forging of a ball, respectively. Annealed aluminium 1100 workpieces are used in both examples. For the finite element analysis, uniaxial compression tests are first performed to provide the material properties. The tests generate elastic moduli and two sets of stress-strain curves (quasi-static and constant strain rate), which are used to establish a rate-dependent material model for input. For both examples 2 and 3, comparisons between the experimental and finite element simulation results for the forming force vs. die displacement relations and also for the deformed configurations show good agreement. The versatility of finite element methods allows for displaying detailed knowledge of the metal forming process, such as the distributions of temperature rise, yield stress, effective stress, plastic strain, plastic strain rate, forming forces and deformed configurations, etc. at any instance during the forming process.