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On the dead-zone formation and limit analysis in axially symmetric extrusion. (English) Zbl 1005.74024

Summary: For axisymmetric direct and indirect extrusion, we propose a kinematically admissible velocity field based on a simple radial flow field combined with asymptotic behaviour of real velocity field near a velocity discontinuity surface. We investigate the influence of extrusion ratio on the shape of dead zone and on the extrusion pressure. The obtained upper bound on the extrusion pressure is compared with other solutions. It is shown that the use of the asymptotic velocity field slightly improves the prediction of extrusion pressure in comparson with other solutions based on radial flows. The main advantages of the proposed approach are that it is applicable to a class of processes, and that it accounts for the behaviour of real velocity field in the vicinity of velocity discontinuity surfaces/maximum friction surfaces where various physical effects like local heating, recrystalization, and transformation occur.

MSC:

74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
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