### Abstract

The 2-D problem of interacting periodic set of edge dislocations and point forces with planar traction-free surface of semi-infinite elastic solid at the nanoscale is considered. Complex variable based technique and Gurtin-Murdoch model of surface elasticity, which leads to the hypersingular integral equation in surface stress, are used. The solution of this equation and explicit formulas for stress field (Green functions) are obtained in terms of Fourier series. The detailed numerical investigation of stress field induced by the dislocations at the nanometer distance from the surface and the force acting on each dislocation in classical and non-classical (with surface stress) solutions is presented. It is shown that formulas derived for the periodic set of dislocations can be applied to the analysis of the interaction of a single dislocation with the surface as well. The fundamental solutions obtained in the work can be used for applying the boundary integral equation method to an analysis of defects such as cracks and inhomogeneities, periodically distributed at the nanometer distance from the boundary. (C) 2017 Elsevier Ltd. All rights reserved.

Original language | English |
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Pages (from-to) | 423-435 |

Number of pages | 13 |

Journal | Engineering Fracture Mechanics |

Volume | 186 |

DOIs | |

Publication status | Published - Dec 2017 |

### Cite this

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**A periodic set of edge dislocations in an elastic semi-infinite solid with a planar boundary incorporating surface effects.** / Grekov, M. A.; Sergeeva, T. S.; Pronina, Y. G.; Sedova, O. S.

Research output

TY - JOUR

T1 - A periodic set of edge dislocations in an elastic semi-infinite solid with a planar boundary incorporating surface effects

AU - Grekov, M. A.

AU - Sergeeva, T. S.

AU - Pronina, Y. G.

AU - Sedova, O. S.

PY - 2017/12

Y1 - 2017/12

N2 - The 2-D problem of interacting periodic set of edge dislocations and point forces with planar traction-free surface of semi-infinite elastic solid at the nanoscale is considered. Complex variable based technique and Gurtin-Murdoch model of surface elasticity, which leads to the hypersingular integral equation in surface stress, are used. The solution of this equation and explicit formulas for stress field (Green functions) are obtained in terms of Fourier series. The detailed numerical investigation of stress field induced by the dislocations at the nanometer distance from the surface and the force acting on each dislocation in classical and non-classical (with surface stress) solutions is presented. It is shown that formulas derived for the periodic set of dislocations can be applied to the analysis of the interaction of a single dislocation with the surface as well. The fundamental solutions obtained in the work can be used for applying the boundary integral equation method to an analysis of defects such as cracks and inhomogeneities, periodically distributed at the nanometer distance from the boundary. (C) 2017 Elsevier Ltd. All rights reserved.

AB - The 2-D problem of interacting periodic set of edge dislocations and point forces with planar traction-free surface of semi-infinite elastic solid at the nanoscale is considered. Complex variable based technique and Gurtin-Murdoch model of surface elasticity, which leads to the hypersingular integral equation in surface stress, are used. The solution of this equation and explicit formulas for stress field (Green functions) are obtained in terms of Fourier series. The detailed numerical investigation of stress field induced by the dislocations at the nanometer distance from the surface and the force acting on each dislocation in classical and non-classical (with surface stress) solutions is presented. It is shown that formulas derived for the periodic set of dislocations can be applied to the analysis of the interaction of a single dislocation with the surface as well. The fundamental solutions obtained in the work can be used for applying the boundary integral equation method to an analysis of defects such as cracks and inhomogeneities, periodically distributed at the nanometer distance from the boundary. (C) 2017 Elsevier Ltd. All rights reserved.

KW - Edge dislocations

KW - Point forces

KW - Green functions

KW - Surface stress

KW - Nanomechanics

KW - CIRCULAR NANO-INHOMOGENEITIES

KW - STRESS-FIELDS

KW - EFFECTIVE STIFFNESS

KW - ARRAYS

KW - NANOSCALE

KW - TENSION

KW - ENERGY

KW - MULTILAYER

KW - INCLUSION

KW - EQUATION

U2 - 10.1016/j.engfracmech.2017.11.005

DO - 10.1016/j.engfracmech.2017.11.005

M3 - статья

VL - 186

SP - 423

EP - 435

JO - Engineering Fracture Mechanics

JF - Engineering Fracture Mechanics

SN - 0013-7944

ER -