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Stress field in ceramic material containing threefold symmetry inhomogeneity

Abstract

The stress concentration and distribution around an inhomogeneity of threefold symmetry in a polycrystalline ceramic matrix is considered. The perturbation method in the theory of plane elasticity is used to solve the problem of a nearly circular inhomogeneity of threefold symmetry under remote loading in the first-order approximation. The solution was specified to the uniaxial tension of convex and concave rounded triangular inhomogeneities. The stress concentration on the interface as well as the stress distribution in both inhomogeneity and matrix along the inhomogeneity symmetry axes are studied and discussed in detail. The numerical results, obtained analytically with the first-order approximate solution, are compared with those of finite-element calculations.

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Acknowledgements

A. B. Vakaeva and M. A. Grekov acknowledge the Russian Foundation for Basic Research (RFBR, Project 18-01-00468, Mechanics of surface phenomena, superficial and subsurface defects in a solid body) for the support in providing the analytical calculations of stress distribution around a triple-junction inhomogeneity. S. A. Krasnitckii and M. Yu. Gutkin acknowledge the Russian Science Foundation (RSF, Project 18-19-00255, Mechanics of bulk functional nanoceramics and ceramic nanocomposites) for the support in the invention of the theoretical model of triple junction inhomogeneities in ceramics and numerical finite-element modeling of the corresponding problem.

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Correspondence to Aleksandra B. Vakaeva.

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The research was supported by Russian Foundation for Basic Research under Grant 18-01-00468 and Russian Science Foundation under Grant 18-19-00255.

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Vakaeva, A.B., Krasnitckii, S.A., Grekov, M.A. et al. Stress field in ceramic material containing threefold symmetry inhomogeneity. J Mater Sci 55, 9311–9321 (2020). https://doi.org/10.1007/s10853-020-04675-7

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  • DOI: https://doi.org/10.1007/s10853-020-04675-7