Numerical simulation of ductile shear localization: Plastic‐flow network and slip‐line field

Abstract

SUMMARYThe development of plastic-flow network (PFN) in plane-strain elastoplastic medium indented locally is simulated using the finite element method, in which the von Mises criterion and a constitutive relation with post-yield softening are used. The results of simulations show that the development process of PFN, which is composed of two families of plastic-flow belts (i.e. ductile shear zones or shear bands) intersecting each other, includes the stages of locally-compacting (I), PFN-spreading (IIa + IIb) and surface-bulging (III). PFN is similar to but different from the traditional slip-line network (slip-line field) that the various solutions of slip-line field correspond only to some critical states of PFN. PFN occurring in elastoplastic medium can be considered as a PFN in viscoplastic medium with high viscosity or high strain rate and both of them are identical in some basic aspects, such as the conjugate angles equal to or greater than 90 • , the direction of the maximum compressive stress in coincidence with the bisector of conjugate angle, the evolution of triangular compacted area, the ingeneration of discontinuity, the weakening effect of the belts and the plastic-flow background of PFN. The simulations of the simplified models stated in this paper provide a basis for the further studies of numerical simulations of PFN, especially those in viscoplastic medium.

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