Numerical simulations of dynamic plastic shear instability under conditions of plane strain

Abstract

The present paper presents a numerical analysis for the edgewise propagation of plastic instability from the tip of a pre-existing semi-infinite 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 plane strain conditions. The simulations take into account finite deformations, 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 rates is employed. In order to investigate the effects of material parameters on the initiation and progression of plastic instability, a series of numerical simulations are conducted by varying the material model parameters that govern material strain hardening, strain rate sensitivity and thermal softening. Additionally, simulations assuming fully adiabatic conditions and those incorporating heat conduction are carried out separately.The results of the simulations confirm the existence of an active plastic zone ahead of the propagating plastic shear instability. In the active plastic zone the gradients in flow stress, the plastic strains, the plastic strain rates and temperature are relatively small in the direction along the propagation of the shear instability as compared to the direction normal to it. The region behind the propagating 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, in the localized region just ahead of the notch tip, the equivalent plastic strain rate after an initial increase is observed to decrease with the applied shearing deformation. The decrease in both the flow stress and the equivalent plastic strain rate leads to a non-zero monotonically decreasing dissipation in the vicinity of the notch tip. Moreover, the plastic dissipation reaches a maximum just behind the tip of the propagating shear instability. Moreover, the results of these simulations indicate that the initiation and progression of the plastic instability are significantly affected by changes in the strain hardening parameter and the strain rate sensitivity of the material. Enhanced strain rate sensitivity is observed to drastically retard the initiation and the progression of plastic instability, whereas the reduced strain hardening results in a considerable decrease in the time required for the initiation of plastic instability and consequently an increase in the overall growth of the plastic instability. In an attempt to characterize the energy absorbed by the material during the development of the plastic shearing instability, J-integral values are calculated for the various material models employed in the present study. It is observed that the J-integral is the highest for the material showing the smallest progression of the plastic instability (material model with enhanced strain rate sensitivity), and lowest for the material showing the largest extension of plastic instability (material model with reduced strain hardening coefficient). These observations reiterate the concept of shear band toughness introduced by Grady (1992).