On the minimization of strain energy in the martensitic transformation of titanium

Abstract

On the basis of Eshelby theory, we have devised a method of predicting various features of martensitic transformation that lead to the minimization of total strain energy. In addition to elastic strain energy considered in previous works, plastic relaxation strain (PRS) concept is introduced in order to relieve the high internal stress due to martensitic transformation. It is postulated that the minimization of the elastic strain energy and the plastic work from the operation of a PRS system dictates the morphology and orientation of a transformation product and the amount and type of the PRS. The theory was applied to the case of martensitic transformation in Ti. In order to reduce the elastic strain energy resulting from transformation, a total of 84 glide and twin systems were evaluated as PRS. For oblate spheroids with aspect ratio less than 0.01, {101̄1} 〈1̄012〉 twin, {101̄1} 〈1̄123〉 glide and {112̄2} 〈1̄123〉 glide or twin systems produced strain energy minima at shear strain of about 2%, although crystal plasticity data of Paton and Backofen rules out the latter twin system. Theoretical prediction on habit plane, shape shear, orientation relationship, the amount and type of PRS, etc. are in excellent agreement with experimental observations.