Equilibrium shapes of coherent precipitates near a surface

•The square-to-rectangle shape transition of a strained precipitate is analyzed.•The effects of anisotropic misfit strain and matrix surface are considered.•Far from the surface, the square shape is favored.•Near a matrix free-surface, the precipitate aligns perpendicular to it.•Near an interface wi...

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Bibliographic Details
Published inMechanics of materials Vol. 117; pp. 22 - 31
Main Author Colin, Jérôme
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.02.2018
Elsevier
Subjects
Acoustics
Automatic
Biomechanics
Chemical Sciences
Electric power
Electromagnetism
Energy methods
Engineering Sciences
Fluid mechanics
Linear elasticity
Material chemistry
Materials and structures in mechanics
Mathematical Physics
Mechanics
Micro-mechanics
Morphology
Physics
Polymers
Precipitates
Quantum Physics
Reactive fluid environment
Thermics
Vibrations
Energy methods
Micro-mechanics
Linear elasticity
Precipitates
Morphology
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Summary:•The square-to-rectangle shape transition of a strained precipitate is analyzed.•The effects of anisotropic misfit strain and matrix surface are considered.•Far from the surface, the square shape is favored.•Near a matrix free-surface, the precipitate aligns perpendicular to it.•Near an interface with a stiffer solid, the precipitate aligns parallel to it. [Display omitted] The shape stability of a two-dimensional precipitate embedded in a matrix has been theoretically investigated when it is strained due to an anisotropic lattice mismatch between the matrix and the precipitate. In the case of a semi-infinite matrix, the precipitate is found to align perpendicularly to the free-surface direction when both lattice mismatches are equal. When the misfit is anisotropic, the precipitate far from the free-surface always align in the direction of lower misfit in absolute value. When both effects of misfit anisotropy and elastic relaxation due to the free-surface oppose, a critical distance between the precipitate and the free-surface may exist below which the precipitate, initially orientated in parallel with the surface, align along the direction perpendicular to it. The case of a precipitate located near an interface between two elastically inhomogeneous phases is also discussed and the shape modification of the precipitate due to the shear moduli has been characterized.
ISSN:0167-6636
1872-7743
DOI:10.1016/j.mechmat.2017.10.007