Analysis of plasticity theory equations of powder metal systems

E. S. Makarov ; A. E. Gvozdev ; G. M. Zhuravlev ; A. G. Kolmakov ; A. N. Sergeev ; S. V. Sapozhnikov ; A. D. Breki ; D. V. Maliy ; N. N. Dobrovolsky

Čebyševskij sbornik, Tome 19 (2018) no. 1, pp. 152-166.

Résumé

The paper provides the review of calculation method and basic parameters of moulding processes in dilatant materials which are typical representatives of powder metal systems of different chemical compositions. They are based on mathematical models that use not only qualitative explanation, but also quantitative description of the dilatancy effect. The work shows the complete system of basic plasticity theory equations of the rigid-plastic isotropic dilatant media. It considers an example of the steady-state plastic flow calculation under conditions of axisymmetric deformation. It is shown that for axisymmetric deformation the equations relative to velocity vector projection on the characteristic directions are similar to the equations for planar deformation. It is established that the current yield conditions with varying degrees of accuracy describe the types of dilatancy (loosening and compaction). Therefore, for a more precise solution of some problems, it is necessary to refine the mathematical models of the yield condition. For some processes of plastic shaping when solving the system of equations of dilatant media, it is expedient to represent the flow conditions in the form of separate regions: hyperbolic, parabolic and elliptic.

Détail

Keywords: dilatant medium, axisymmetric deformation, complete system of equations, condition of fluidity, characteristics of the yield curve, powder metal system.

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