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Effects of surface/interface elasticity on the screw dislocation-induced stress field in an elastic film–substrate system

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Abstract

In the analysis of continuum-based models describing the dislocation mechanism for a film–substrate system, it is customary to treat the surface of the film as ‘traction-free’ or ‘perfectly bonded’ to the substrate. For an ultra-thin film, however, the appreciable surface to volume ratio is known to be responsible for considerable surface energies which contribute significantly to the overall deformation of the structure. Consequently, in order to ensure a sufficiently accurate account of the corresponding dislocation behavior, it becomes necessary to incorporate the contribution of surface/interface effects into the description of deformation of the film surface or film–substrate interface. In this paper, we study the effects of surface/interface elasticity on the mechanical behavior of a screw dislocation embedded in a thin film bonded to an elastic substrate. Using conformal mapping techniques, we derive a semi-analytical solution for the dislocation-induced stress field in the film–substrate system. Our results show that when the thickness of the film approaches the nanoscale, failure to incorporate surface/interface elasticity into the description of the corresponding surface or interface may induce significant errors in the stress field and in any predictions involving the mobility of the dislocation. More specifically, we show that whereas the incorporation of surface elasticity with positive shear modulus always relieves the stress concentration on the surface of the film–substrate system, interface elasticity with positive shear modulus can either relieve or intensify the stress concentration (for the film) on the film–substrate interface depending on the stiffness of the substrate. In particular, for an ultra-thin film bonded to a soft substrate, we find that the presence of interface elasticity greatly influences the (unstable) equilibrium position of the dislocation in the film.

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Acknowledgements

Dai appreciates the Natural Science Foundation of Jiangsu Province (Application No. SBK2019040621), a start-up grant of the Nanjing University of Aeronautics and Astronautics and a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions. Schiavone thanks the Natural Sciences and Engineering Research Council of Canada for their support through a Discovery Grant (Grant # RGPIN – 2017 - 03716115112).

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Authors and Affiliations

  1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Ming Dai

  2. Department of Mechanical Engineering, University of Alberta, Edmonton, AB, T6G 1H9, Canada

    Peter Schiavone

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  1. Ming Dai
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Correspondence to Peter Schiavone.

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Dai, M., Schiavone, P. Effects of surface/interface elasticity on the screw dislocation-induced stress field in an elastic film–substrate system. Z. Angew. Math. Phys. 70, 101 (2019). https://doi.org/10.1007/s00033-019-1144-9

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