Analysis of a brittle-ductile transition under dynamic shear loading

Abstract

The competition between brittle and ductile modes of failure is analyzed in a double edge-cracked specimen impacted by a projectile on the cracked side. Full transient analyses under plane strain conditions are carried out, with impact simulated by an imposed normal velocity with a small rise time. The material response is characterized by an elastic—viscoplastic constitutive relation for a porous plastic solid, with adiabatic heating due to plastic dissipation and the resulting thermal softening accounted for. The onset of cleavage is assumed to occur when a critical value of the maximum principal stress is attained. Effects of varying the loading rate and the thermal softening characterization of the material are explored. If the thermal softening rate is sufficiently high, a transition from a brittle failure mode at low loading rates to a ductile failure mode at high loading rates is found, which is quite the opposite of the usual brittle—ductile transition behavior. This prediction for the fracture mode transition is consistent with experimental observations under these loading conditions. Additionally, the failure paths indicated by the calculations are consistent with what is seen in experiments. The mechanism precipitating the brittle—ductile transition is a greater increase in peak strain magnitude than in peak stress magnitude with increased loading rate. When the strains ahead of the crack tip become large enough, thermal softening and possibly porosity-induced softening can lead to a localization of deformation, which limits the peak value of the maximum principal stress so that cleavage does not occur and the failure mode is ductile.