The onset of twinning in metals: a constitutive description

A constitutive approach is developed that predicts the critical stress for twinning as a function of external (temperature, strain rate) and internal (grain size, stacking-fault energy) parameters. Plastic deformation by slip and twinning are considered as competitive mechanisms. The twinning stress is equated to the slip stress based on the plastic flow by thermally assisted movement of dislocations over obstacles, which leads to successful prediction of the slip-twinning transition. The model is applied to body centered cubic, face centered cubic, and hexagonal metals and alloys: Fe, Cu, brasses, and Ti, respectively. A constitutive expression for the twinning stress in BCC metals is developed using dislocation emission from a source and the formation of pile-ups, as rate-controlling mechanism. Employing an Eshelby-type analysis, the critical size of twin nucleus and twinning stress are correlated to the twin-boundary energy, which is directly related to the stacking-fault energy (SFE) for FCC metals. The effects of grain size and SFE are examined and the results indicate that the grain-scale pile-ups are not the source of the stress concentrations giving rise to twinning in FCC metals. The constitutive description of the slip-twinning transition are incorporated into the Weertman–Ashby deformation mechanism maps, thereby enabling the introduction of a twinning domain. This is illustrated for titanium with a grain size of 100 μm.