A constitutive approach was developed that predicted the critical stress for twinning as a function of external (temperature, strain-rate) and internal (grain-size, stacking-fault energy) parameters. Plastic deformation via slip and twinning were considered to be competing mechanisms. The twinning stress was equated to the slip stress based on plastic flow via the thermally assisted movement of dislocations over obstacles; leading to a successful prediction of the slip-twinning transition. The model was applied to body-centered cubic, face-centered cubic, and hexagonal metals and alloys. A constitutive expression for the twinning stress in body-centered cubic metals was developed by considering dislocation emission from a source, and the formation of pile-ups, to be rate-controlling mechanisms. By using an Eshelby-type analysis, the critical size of the twin nucleus and the twinning stress were correlated with the twin-boundary energy; which was directly related to the stacking-fault energy of face-centered cubic metals. The effects of grain size and stacking-fault energy were examined, and the results indicated that grain-scale pile-ups were not the source of the stress concentrations that gave rise to twinning in face-centered cubic metals. The constitutive description of the slip-twinning transition were incorporated into Weertman¯Ashby deformation-mechanism maps, thus permitting the introduction of a twinning domain.

The Onset of Twinning in Metals - a Constitutive Description. M.A.Meyers, O.Vöhringer, V.A.Lubarda: Acta Materialia, 2001, 49[19], 4025-39