NUMERICAL SIMULATIONS OF DYNAMIC PLASTIC SMEAR INSTABILITY UNDER CONDITIONS OF PLANE-STRAIN

The present paper presents a numerical analysis for the edgewise propa gation of plastic instability from the tip of a pre-existing semi-infi nite notch in an otherwise unbounded continuum. The driving force for the shear deformation is provided by an in-plane shear loading pulse. Coupled thermo-mechanical simulations are carried out under fully plan e strain conditions.The simulations take into account finite deformati ons, inertia, heat conduction, thermal softening, strain hardening and strain rate hardening. A combined power law-exponential relation that gives rise to enhanced strain-rate hardening and ultra-high strain ra tes is employed. In order to investigate the effects of material param eters on the initiation and progression of plastic instability, a seri es of numerical simulations are conducted by varying the material mode l parameters that govern material strain hardening, strain rate sensit ivity and thermal softening. Additionally, simulations assuming fully adiabatic conditions and those incorporating heat conduction are carri ed out separately. The results of the simulations confirm the existenc e of an active plastic zone ahead of the propagating plastic shear ins tability. In the active plastic zone the gradients in flow stress, the plastic strains, the plastic strain rates and temperature are relativ ely small in the direction along the propagation of the shear instabil ity as compared to the direction normal to it. The region behind the p ropagating instability exhibits highly localized shear deformation and intense heating. The intense heating results in thermal softening and hence a decrease in the flow stress in this localized region. Also, i n the localized region just ahead of the notch rip, the equivalent pla stic strain rate after an initial increase is observed to decrease wit h the applied shearing deformation. The decrease in both the flow stre ss and the equivalent plastic strain rate leads to a non-zero monotoni cally decreasing dissipation in the vicinity of the notch tip. Moreove r, the plastic dissipation reaches a maximum just behind the tip of th e propagating shear instability. Moreover, the results of these simula tions indicate that the initiation and progression of the plastic inst ability are significantly affected by changes in the strain hardening parameter and the strain rate sensitivity of the material. Enhanced st rain rate sensitivity is observed to drastically retard the initiation and the progression of plastic instability, whereas the reduced strai n hardening results in a considerable decrease in the rime required fo r the initiation of plastic instability and consequently an increase i n the overall growth of the plastic instability. In an attempt to char acterize the energy absorbed by the material during the development of the plastic shearing instability, J-integral values are calculated fo r the various material models employed in the present study. It is obs erved that the.I-integral is the highest for the material showing the smallest progression of the plastic instability (material model with e nhanced strain rate sensitivity), and lowest for the material showing the largest extension of plastic instability (material model with redu ced strain hardening coefficient). These observations reiterate the co ncept of shear band toughness introduced by Grady (1992). (C) 1998 Els evier Science Ltd. All rights reserved.