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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Published in | Mechanics of materials Vol. 117; pp. 22 - 31 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
Elsevier Ltd
01.02.2018
Elsevier |
Subjects | |
Online Access | Get full text |
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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.
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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. |
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ISSN: | 0167-6636 1872-7743 |
DOI: | 10.1016/j.mechmat.2017.10.007 |