New theory for crack-tip twinning in fcc metals

Abstract

Dislocation emission from a crack tip is a necessary mechanism for crack tip blunting and toughening. In fcc metals under Mode I loading, a first partial dislocation is emitted, followed either by a trailing partial dislocation ("ductile" behaviour) or a twinning partial dislocation ("quasibrittle"). The twinning tendency is usually estimated using the Tadmor and Hai extension of the Rice theory. Extensive molecular statics simulations reveal that the predictions of the critical stress intensity factor for crack tip twinning are always systematically lower (20-35%) than observed. Analyses of the energy change during nucleation reveal that twin partial emission is not accompanied by creation of a surface step while emission of the trailing partial creates a step. The absence of the step during twinning motivates a modified model for twinning nucleation that accounts for the fact that nucleation does not occur directly at the crack tip. Predictions of the modified theory are in excellent agreement with all simulations that show twinning. Emission of the trailing partial dislocation, including the step creation, is predicted using a model recently introduced to accurately predict the first partial emission and shows why twinning is preferred. A second mode of twinning is found wherein the crack first advances by cleavage and then emits the twinning partial at the new crack tip; this mode dominates for emission beyond the first twinning partial. These new theories resolve all the discrepancies between the Tadmor twinning analysis and simulations, and have various implications for fracture behaviour and transitions.

Stress-dependence of generalized stacking fault energies

“…In addition, the Rice theory for dislocation emission is typically somewhat lower than detailed simulation studies [4] and so "opening softening" would lead to further deviations between theory and simulation. The present authors also recently introduced a new theory/analysis for cracktip dislocation emission and twinning that agrees very well with simulations of the critical stress intensity factor without including any "opening softening" effect [4,9]. These factors motivate 75 us to revisit the measurement/computation of the stress dependence of the GSFE more thoroughly than in earlier works.…”

“…The GSFE is also recognized as a crucial material property for describing nanoscale plasticity, especially dislocation nucleation processes such as dislocation emission (i) from a crack tip [3,4], (ii) from a grain boundary [5,6], (iii) during nanoindentation [7], and (iv) to create crack-tip twinning 40 [8,9].…”

Atomistic modeling of fracture

“…111 110 crystal orientation and at T=0 K, the only possible process is the emission of the twinning partial dislocation, which has the same character as the first partial but gliding on an immediately adjacent slip plane [63]. This crack-tip twinning can be predicted using the theory recently proposed by the authors [64], which is an extension of the Tadmor and Hai theory [63]. The remote critical stress intensity factor for crack-tip twinning K Ie twin in the presence of the first partial dislocation is where γ utf is the unstable twinning fault energy, ( )…”

Intrinsic fracture behavior of Mg–Y alloys

“…A full dislocation can glide far away from the crack tip. The analysis of [20] extends the original instability-based emission theory to include the second partial dislocation emission. For the case where a full dislocation is formed, an analytic estimate of the stress intensity for the emission of the trailing partial is where g ssf e is the stable stacking fault energy of the emission plane, and j trail is the inclination of the trailing dislocation Burgers vector with respect to the crack front normal on the emission plane.…”