An analysis of frictional effects in non-stationary contact problems for metal forming simulations

Doctoral Thesis


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The finite element method (FEM) is widely used for the simulation of metal forming processes and has been successfully used in contact problems which arise in processes such as deep-drawing, punching, extrusion and rolling. All these processes involve friction between the contact surfaces: the sheet-metal workpiece and the toolpieces. The model of friction is thus an important part of any simulation of metal forming processes. Most FEM codes use a friction model that assumes that the contact surface is a plane. Attempts to address this problem have focused on the convective description of deformation, which has the advantage of being naturally extended to numerical methods like the FEM at the expense of additional computation and numerical complexity. The convective description is used in this work, which focuses on the numerical implementation of the objective measure. The effects of the rotation of the material contact point is taken into account by including objective time derivatives of the slipping (tangential) direction function. The objective rate of the direction function includes the surface spin induced by the rigid motion of a contact point sliding over the tool surface, and the material spin occurring during the elastic-plastic deformation of the blank. This is introduced by adapting the incremental relations of the friction slip. This thesis presents the results of numerical experiment to determine the influence that the rotation and convection of contact points has on the frictional stresses and slipping energy. Four different friction models are implemented within the finite element program ABAQUS and applied to simulations of standardmetal forming benchmark processes: the square-cup and s-rail deep drawing benchmarks of the Numisheet conferences, for which several experimental and numerical results are available to compare with the solution of a finite element simulation. The results for each metal-forming simulation are calculated for different friction models, and are compared and a choice made as to which is the “best” friction model for the process. Further, the reverse problem of determining the values of friction parameters by comparison of simulation and experimental results is performed for these benchmark problems. As there is yet no ideal friction model for all processes that are modelled, finding the most appropriate friction model by numerical means is proposed to improve the quality of a simulation.