Finite Element Upsetting Analysis of a Ring: An Incremental Solution to the Contact Problem
The ring test has been devised to measure friction paratmeters under extreme pressure conditions as in metal forming processes. However, gravely erroneous assumptions are used to develop and interpret the test. The continuum difinition of stress is violated not only by the test theory but also by the current concepts of friction and lubrication. The author has proposed a general solution for the contact problem based primarily on the continuum definition of stress as a local quantity. An experimental procedure, following Bridgman’s shear-compression fracture tests is proposed to measure frictional properties in a new format. The resulting information is introduced in the analysis as explicit displacement or traction boundary conditions. The incremental nature of the nonlinear boundary value problem involving the deforming media in contact is conveniently used to generate a discretized approximation to the state of stress and deformation along the contact surface at the end of each solution increment. An important consequence of this approach is that the symmetry of the stiffness matrix in the finite element analysis is insured, resulting in considerable computational savings. Another advantage of the proposed method is the elimination of non-physical corner stress singularities. Moreover, recognition of the local nature of contact stresses implies that the proposed method is applicable to any geometry of contact.
The finite element analysis of the upsetting of the standard steel ring is carried out using an elastic-plastic finite deformation theory and the new method of contact modeling. Computer graphics are employed to display stress distributions. The results point out the serious shortcomings of the standard ring test and the present friction measurement methods in general. The proposed method may be used in computer-aided design of metal forming processes and in the analysis of many complex boundary value problems involving contact.
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