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Three‐dimensional thermoelastic stresses in off‐axis oriented single crystals with hexagonal symmetry
Author(s) -
Böttcher K.,
Cliffe K. A.
Publication year - 2007
Publication title -
crystal research and technology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.377
H-Index - 64
eISSN - 1521-4079
pISSN - 0232-1300
DOI - 10.1002/crat.200610817
Subject(s) - thermoelastic damping , rotational symmetry , geometry , cauchy stress tensor , tensor (intrinsic definition) , hexagonal lattice , symmetry (geometry) , hexagonal crystal system , coordinate system , materials science , finite element method , stress (linguistics) , crystallography , orientation (vector space) , boundary value problem , physics , chemistry , condensed matter physics , mathematics , mathematical analysis , classical mechanics , thermal , thermodynamics , linguistics , philosophy , antiferromagnetism
A three‐dimensional (3D) thermoelastic stress analysis is carried out on a single crystal with axisymmetric geometry but with a hexagonal crystallographic symmetry. The crystallographic orientation is off‐axis with respect to the cylindrical coordinate system. By applying a Fourier series expansion with respect to the rotational angle ϕ of the cylindrical coordinates, the 3D boundary value problem is reduced to a sequence of 2D ones on the meridian plane, which are solved by the finite‐element method. In our example, the off‐axis orientation is towards a direction of high symmetry, and therefore only four of the six stress tensor components are non‐zero. In the end, the stress tensor is projected onto the slip system of the crystal. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)