Abstract
The validity of our nucleation model of deformation twinning previously proposed for fcc metals has been quantitatively examined to determine the stacking fault energy γSF from the twinning stress τT, with particular attention to the orientation dependence of τT of pure copper crystals deformed in tension at 4.2 K. Main results obtained are summarized as follows:
(1) τT in Cu crystals is decreased as the specimen axis approaches [111] from [100] when twinning occurs in stage III, while in stage II little affected by the orientation. This orientation dependence, consistent with that previously observed in pure Ag and Cu alloy crystals, can be quantitatively explained by our model.
(2) The value of γSF of pure Cu at 4.2 K has been evaluated as 43.5±2 mJ/m2 from the twinning stress τT by using the equation derived from our model.
(3) Upon nucleation of twins, the critical internal stress acting on the twinning dislocations, which arises from a dislocation pile-up in our model, is about 1.3 times as large as the applied stress in Cu crystals tested at 4.2 K. This ratio of internal stress to applied stress is the same as that previously reported in Ni-based alloys.
(4) By using this stress ratio, the equation derived from our model is simplified with good approximation as γSF=ξ(R)τTbS, where ξ(R) is a parameter depending only on the specimen orientation and bS the Burgers vector of a Shockley partial dislocation.
(5) This simplified formula can be applied to the case in which twinning occurs not later than early stage III where the relief of internal stress is ignored. Under this condition, the value of γSF in fcc metals and alloys is directly determined from τT in specimens oriented near [211] by a formula, γSF=2τTbS.
