The preferred habit of a coherent thin-plate inclusion in an anisotropic elastic solid

Journal Article · Sat Aug 01 04:00:00 EDT 1987 · Acta Metall.; (United States)

DOI:https://doi.org/10.1016/0001-6160(87)90046-0· OSTI ID:5573411

Kostlan, E; Morris, Jr, J W

The work reported here was undertaken to find algebraic equations for the preferred habits of coherent thin-plate inclusions in anisotropic media on the assumption that the inclusion and matrix can be treated as linear elastic continua. The preferred habit minimizes the elastic energy, which depends on the elastic constants of the inclusion and the transformation strain connecting the lattices of the inclusion and the matrix. The paper presents four principal results concerning the preferred thin-plate habit. First the mathematical conditions that determine the preferred habit are derived in compact form. These conditions are always satisfied when the transformation strain is dyadic and the habit is perpendicular to a vector of the dyad, reproducing a result that is given by Khatchaturyan and included in the crystallographic theory of precipitate habits. The extremal conditions are solved for orthorhombic symmetry, that is, when the elastic constants of the inclusion have orthorhombic symmetry with respect to the principal axes of the transformation stress. The results incorporate isotropic, cubic, hexagonal and tetragonal (type II) symmetries. They are specialized to determine the minimum-energy habit as a function of the transformation strain for three classes of inclusions: isotropic inclusions, cubic inclusions with tetragonal transformation strains, and hexagonal inclusions with hexagonal transformation strains. Finally it is shown by counter-example that there is no general algebraic solution for systems of arbitrary symmetry.

• Research Organization: Mathematical Sciences Research Institute and Center for Advanced Materials, Lawrence Berkeley Lab., and Dept. of Materials Science and Mineral Engineering, Univ. of California, Berkeley, CA 94720
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 5573411
• Journal Information: Acta Metall.; (United States), Journal Name: Acta Metall.; (United States) Vol. 35:8; ISSN AMETA
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
360602* -- Other Materials-- Structure & Phase Studies
ANISOTROPY
CRYSTAL LATTICES
CRYSTAL STRUCTURE
CRYSTALLOGRAPHY
CUBIC LATTICES
ELASTICITY
HEXAGONAL LATTICES
INCLUSIONS
ISOTROPY
MECHANICAL PROPERTIES
ORTHORHOMBIC LATTICES
PLATES
PRECIPITATION
SEPARATION PROCESSES
SOLIDS
STRAINS
STRUCTURAL CHEMICAL ANALYSIS
TENSILE PROPERTIES
TETRAGONAL LATTICES