Quasi-equilibrium modeling of the toughness transition during semibrittle cleavage

A discretized dislocation model is used to assess the quasi-state equilibrium, crack tip emission and shielding of near-tip dislocations for Mo single crystals. As in a previous study for Fe-3 wt% Si, based partly on the Rice-Thomson criterion [12], this model leads to a failure prediction for Mo both consistent with the absence of an expected dislocation free zone and the observed toughness transition over the test temperature range. While cleavage is the failure mode in the semibrittle regimes of these two b.c.c. crystals, K_Ic values vary from 5 up to 60 MPa-m^1/2 with an increase in test temperature. The equilibrium solution for both metals from the discrete dislocation model is reconnected with ordinary continuum theory through the CTOD and plastic zone size, as well as Weertman's hypothesis [19] of the nonredundant/redundant dislocation decomposition for near-tip microplasticity. The similarities in zeroth order successive approximation solutions derived for these two metals, with very disparate elastic anisotropies, suggests that such approaches may also be applicable to semibrittle ordered intermetallics.