On transformation shear of precipitated zirconia particles

A model is proposed to investigate the transformation shear of the precipitated zirconia particles which undergo a stress-induced lattice transformation from tetragonal to monoclinic symmetry. Kinematically admissible twinning planes and the corresponding twinning elements are determined according to the continuum theory of dispacive phase transformation. It is postulated that only one twinning mode prevails in each transformed particle and that the minimization of elastic strain energy change dictates the morphology of the transformed variants. The transformation shear is determined by the twinning mode and the volume fraction of the corresponding variant. Numerical calculations show that each of the six kinematically admissible twinning modes may be kinematically favorable and therefore operate in a constrained particle. The actual transformation shear in a transformed particle is shown to be dependent on the transformation stress, on the particle shape as well as on the lattice orientation relative to the principal axes of the ellipsoidal particle.     

Numerical study of transverse lattice waves connected with martensitic transformation

The behavior of the transverse lattice wave connected with the nucleation process of martensite is studied, taking into account the anharmonicity, by use of one-dimensional model for the crystal. The key factor which determines the behavior of the transverse lattice waves according to the model is its amplitudeA with respect to the critical amplitudeA _c. As far asA < A _c, the presence of the transverse lattice wave does not lead to the initiation of the martensite. Depending on the variation ofA andA _c with temperature, the model suggests two alternative processes for the initiation of the martensitic transformation. 1) In case the variation ofA _c with temperature is larger than the variation ofA with temperature, the transverse lattice wave develops into the stable nuclei of the martensite, as soon asA _c becomes smaller thanA with decrease of temperature. 2) In case the variation ofA with temperature is larger than the variation ofA _c with temperature, the transverse lattice wave represents the heterophase fluctuation whenA « A _c. The stable martensite is formed with the reduction ofA as temperature is reduced. The presently available experimental data suggest the process 1) as the nucleation mechanism of the martensite. The prominent role of the interface energy between the martensite and the austenite in determining both the structure of the martensite and the dispersion relationship of the transverse lattice wave in the austenite is pointed out.