A sensitivity analysis for the optimal design of metal-forming processes

A major objective in metal-forming processing is the optimum selection of process conditions in the design stage processes given the material state and the geometry of the final product, conditions on the initial workpiece and possibly some restrictions on the processes. Since the required process conditions are input to the direct forming analysis, the design of forming processes usually consists of the repeated trial and error use of direct modeling techniques. Here, process conditions refer to die surfaces, die lubrication conditions, preform selection and the selection of the required ram forces and velocities. In this work, a sensitivity analysis for large deformation hyperelastic viscoplastic solids is presented that is consistent with the kinematic analysis and the constitutive integration scheme used in the updated Lagrangian method for solving the direct deformation problem. The method is developed with the problem of die design in metal-forming processes in mind. As such, special attention is given to the modeling of the complex boundary conditions that result in the die-workpiece interface. The effectiveness of the method is demonstrated by solving an extrusion axially symmetric die design problem. In particular, an extrusion die is designed such that the material state in the final product has the least possible standard deviation.