Publication detail

An asymptotic analysis of crack initiation from an interfacial zone surrounding the circular inclusion

PROFANT, T. HRSTKA, M. KLUSÁK, J.

Original Title

An asymptotic analysis of crack initiation from an interfacial zone surrounding the circular inclusion

Type

journal article in Web of Science

Language

English

Original Abstract

A geometrically simplified plane elasticity problem of a finite small crack emanating from a thin interfacial zone surrounding the circular inclusion situated in the finite bounded domain is investigated. The inclusion can model a particle in a composite material. The crack is modelled using the distribution dislocation technique, which represents the so called inner solution or boundary layer of the studied problem. Its application is conditioned by the knowledge of the fundamental solution of the dislocation interacting with the inclusion and its interfacial zone. The fundamental solution is based on the application of Muskhelishvili complex potentials in the form of the Laurent series. The coefficients of the series are evaluated from the compatibility conditions along the interfaces of the inclusion, the interfacial zone and the matrix. Another supplement of the fundamental solution is its utilization for the so-called outer solution, which is the solution of the boundary integral method approximating the stress and strain relations along the external boundary of the domain containing the inclusion. The asymptotic analysis is introduced at the point of crack initiation to control the mismatch between the outer and the inner solutions along the external boundary of the studied domain. The asymptotic analysis results in the evaluation of the stress intensity factors as the leading terms of the asymptotic series expressed from the stress distribution near the crack tip, which lies in the matrix. The topological derivative is used to approximate the energy release rate field associated with the perturbing of the matrix by the finite small crack emanating from the interfacial zone. The assessed values of the energy release rate allow one to study the influence of the interfacial zone dimension and elastic properties on crack initiation under the conditions of finite fracture mechanics.

Keywords

Crack interaction; Muskhelishvili complex potentials; Interfacial zone; Dislocation; Circular inclusion; Fundamental solution; Topological derivative

Authors

PROFANT, T.; HRSTKA, M.; KLUSÁK, J.

Released

15. 1. 2019

Publisher

Elsevier

ISBN

0263-8223

Periodical

COMPOSITE STRUCTURES

Year of study

208

Number

1

State

United Kingdom of Great Britain and Northern Ireland

Pages from

479

Pages to

497

Pages count

19

URL

https://www.sciencedirect.com/science/article/pii/S0263822318304847

BibTex

@article{BUT152042,
  author="Tomáš {Profant} and Miroslav {Hrstka} and Jan {Klusák}",
  title="An asymptotic analysis of crack initiation from an interfacial zone surrounding the circular inclusion",
  journal="COMPOSITE STRUCTURES",
  year="2019",
  volume="208",
  number="1",
  pages="479--497",
  doi="10.1016/j.compstruct.2018.10.020",
  issn="0263-8223",
  url="https://www.sciencedirect.com/science/article/pii/S0263822318304847"
}