The strain energy of a spheroidal inclusion and its application to b.c.c.-h.c.p. martensitic transformation

Abstract

The strain energy of a spheroidal inclusion was evaluated exactly using the Eshelby theory. Numerical results for an oblate spheroid are presented in a parametric form in terms of the transformation strain tensor. Using atomistic transformation mechanisms, the transformation strain was determined for b.c.c.-h.c.p. martensitic transformation in Ti and its alloys. The lattice correspondence satisfied the Burgers relationship and the c a -ratio in the product phase was taken as 1.586. The habit plane was predicted on on the basis of the strain energy minimization principle. Results of the calculation indicate that the strain energy is minimized when the morphology of h.c.p. Ti martensite is a thin disc-shaped inclusion lying on a plane close to (11 X) B , where X is equal to 1.2–1.3. This habit plane is in excellent agreement with experimental observations. The present approach is discussed in detail and compared with the crystallographic theory based on the invariant plane strain hypothesis.