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Residual stress and strain energy in composites induced by transformed coated circular inhomogeneities

Marinos A. Kattis and Elli Gkouti

Vol. 18 (2023), No. 1, 1–18

The residual stress and strain energy in coated fiber composites induced by a transformation strain in the fiber coatings are theoretically studied. The relative analysis utilizes a simplified elasticity model consisting of a coated circular inhomogeneity embedded in an unbounded matrix, with the coating undergoing a uniform stress-free transformation strain. The distribution of the residual stress in and around the coating and portioning of the elastic energy in the matrix, coating and inhomogeneity are derived and their dependence on the material and geometric parameters of the three-phase body is investigated. It shown that within the coating and irrespective of the coating hardness, the magnitude of the tangential stress is higher than that of the others and the total elastic energy is distributed almost entirely between coating and matrix with an extremely small amount stored in the inhomogeneity. As the coating thickness becomes very small compared to the size of the inhomogeneity, the only nonvanishing stress component in the coating is the tangential one, with the total elastic energy accumulating in the coating. In this special case, the thin coating approaches the behavior of a membrane interface with surface tension, which is located between a circular nano-inhomogeneity and an elastic matrix, both consisting of dissimilar crystalline materials. The surface tension of the membrane interface is represented by the resultant of the tangential stress on the coating thickness, coming from the lattice mismatch strain of the bonded materials.

coated inhomogeneity, transformation strain, stress concentration, elastic energy
Received: 10 May 2020
Revised: 17 September 2022
Accepted: 14 November 2022
Published: 24 March 2023
Marinos A. Kattis
School of Rural and Surveying Engineering
National Technical University of Athens
Elli Gkouti
School of Rural and Surveying Engineering
National Technical University of Athens