Revisit of the shape and orientation of precipitates with tetragonal transformation strains that minimise the elastic energy

A. Tordjman, A. Wasserblat, R. Z. Shneck

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

The selection of the shape and orientation of precipitates with tetragonal misfit (transformation) strains that minimise the elastic energy is revisited. The complex map of preferred shapes suggested by Kaganova and Roitburd for inhomogeneous isotropic materials is extended to materials with cubic symmetry and for systems that compromise with the surface energy of close-packed planes. Several shape transitions are explained from the kinematics of precipitates with tetragonal transformation strains in solid matrices. Plate shaped precipitates are associated with minimum elastic energy in homogenous systems and for soft precipitates, in accordance with the theorem of Khachaturyan. We explain how compact shapes like rods and spheres arise when the matrix is softer than the precipitate. Analytic estimations are derived to determine the preferred shapes based on the difference between the elastic stiffness of the matrix and the precipitate. When the transformation strains differ in sign, they give rise to a large lattice rotation. This lattice rotation is necessary for the formation of twins by equivalent variants of the transformation strain.

Original languageEnglish
Pages (from-to)927-954
Number of pages28
JournalPhilosophical Magazine
Volume100
Issue number8
DOIs
StatePublished - 17 Apr 2020

Keywords

  • Anisotropic properties
  • computational mechanics
  • equilibrium shape
  • precipitation

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