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Edge dislocation in
a thin film with curvature-dependent surface tension
Junfeng Lu, Ming Dai and Peter Schiavone |
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Vol. 20 (2025), No. 4, 471–487
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DOI: 10.2140/jomms.2025.20.471
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Abstract |
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We explore the effects of curvature-dependent surface tension on the elastic behavior of a line edge dislocation embedded in a free-standing thin film. The dislocation line is assumed to be parallel to the surface of the film, while the entire system is confined to plane strain deformations. The total surface tension is treated as the sum of a constant initial part arising from the originally flat surface of the film and a configuration-dependent part proportional to the curvature of the deformed surface of the film. We employ the complex variable formalism of elasticity and develop a series-based solution procedure to determine the dislocation-induced stress field in the film subjected to the nonclassical boundary conditions related to the curvature-dependent surface tension. The image force, describing the mobility of the dislocation, is also represented in terms of the obtained coefficients of the series. By setting the curvature-dependence parameter of surface tension to zero, our procedure recovers accurately the known analytic results in the literature for an edge dislocation in an elastic half-plane with constant surface tension. Numerical examples are presented for illustrating the influence of the curvature-dependence parameter of surface tension on the local stress field near the surface of the film and the image force. It is shown that as the thickness of the film decreases to a few nanometers, the curvature dependence of surface tension always contributes significantly to the determination of the stress concentration around the surface of the film irrespective of the direction of the Burgers vector of the dislocation. In contrast, however, it is found that even for a few-nanometer-thickness film the influence of the curvature dependence of surface tension on the image force becomes notable only when the Burgers vector is at a large angle to the surface of the film (for example, more than ) and simultaneously the distances from the dislocation to the two surfaces of the film differ significantly (for example, by a factor of three or more). |
Keywords
thin film, surface tension, curvature dependence, edge
dislocation, image force
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Milestones
Received: 2 September 2025
Revised: 16 October 2025
Accepted: 19 October 2025
Published: 1 November 2025
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Authors |
| Junfeng Lu | |
| School of Electrical and Mechanical
Engineering, Jinling Institute of Technology Nanjing, 211169 China |
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| Ming Dai | |
| State Key Laboratory of Mechanics
and Control for Aerospace Structures Nanjing University of Aeronautics and Astronautics Nanjing, 210016 China |
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| Peter Schiavone | |
| Department of Mechanical
Engineering University of Alberta Edmonton AB T6G 1H9 Canada |
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| © 2025 MSP (Mathematical Sciences Publishers). |
