Sensitivity analysis and shape optimization for preform design in thermo-mechanical coupled analysis

In complex forging processes, it is essential to "nd the optimal deformation path and the optimal preform shape that will lead to the desired "nal shape and service properties. A sensitivity analysis and optimization for preform billet shape in thermo-mechanical coupled simulation is developed in this work. Non-linear sensitivity analysis of temperatures, #ow-stresses, strains and strain-rates are presented with respect to design variables. Both analytical and "nite-di!erence gradients are employed to validate the e!ectiveness of sensitivity analysis developed in this work. Numerous iterations of coupled thermo-mechanical analysis are performed to determine an optimum preform shape based on a given criterion of minimizing the objective function on e!ective strain variance within the "nal forging. The design constraints are imposed on die under"ll, material scrap, folding defects and temperatures. In addition, a method for material data processing is given in order to determine the #ow stress and its derivatives. The shape optimization scheme is demonstrated with the preform designs of an axisymmetric disk and a plane strain problem.