A Computational Scheme for the Interaction between an Edge Dislocation and an Arbitrarily Shaped Inhomogeneity via the Numerical Equivalent Inclusion Method

P. Li, X. Zhang, D. Lyu, X. Jin*, Leon M Keer

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

The interactions between dislocations and inhomogeneity may play an important role in strengthening and hardening of materials. The problem can be solved analytically only for limited cases of simple geometry. By employing the recently developed numerical equivalent inclusion method, this work presents an effective computational scheme for studying the stress field due to an edge dislocation in the vicinity of an arbitrarily shaped inhomogeneity. The inhomogeneity is treated as an equivalent inclusion that is numerically discretized by rectangular elements. The mismatch between the matrix and the inhomogeneity materials are formulated through Dundurs’ parameters for numerical stability and robustness. The proposed method can efficiently and accurately evaluate the elastic field of the equivalent inclusion with the assistance of a fast Fourier transform based algorithm, constituting an essential refinement of the existing approach in the dislocation-inhomogeneity literature. Several benchmark examples are examined to demonstrate the flexibility, efficiency and accuracy of the present method.

Original languageEnglish (US)
Pages (from-to)164-171
Number of pages8
JournalPhysical Mesomechanics
Volume22
Issue number2
DOIs
StatePublished - Mar 1 2019

Fingerprint

Edge dislocations
edge dislocations
inhomogeneity
inclusions
Strengthening (metal)
Convergence of numerical methods
interactions
Fast Fourier transforms
Hardening
numerical stability
Geometry
hardening
stress distribution
flexibility
matrices
geometry

Keywords

  • Dundurs’ parameters
  • arbitrarily inhomogeneity
  • edge dislocation
  • fast Fourier transforms
  • numerical equivalent inclusion method

ASJC Scopus subject areas

  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Surfaces and Interfaces

Cite this

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abstract = "The interactions between dislocations and inhomogeneity may play an important role in strengthening and hardening of materials. The problem can be solved analytically only for limited cases of simple geometry. By employing the recently developed numerical equivalent inclusion method, this work presents an effective computational scheme for studying the stress field due to an edge dislocation in the vicinity of an arbitrarily shaped inhomogeneity. The inhomogeneity is treated as an equivalent inclusion that is numerically discretized by rectangular elements. The mismatch between the matrix and the inhomogeneity materials are formulated through Dundurs’ parameters for numerical stability and robustness. The proposed method can efficiently and accurately evaluate the elastic field of the equivalent inclusion with the assistance of a fast Fourier transform based algorithm, constituting an essential refinement of the existing approach in the dislocation-inhomogeneity literature. Several benchmark examples are examined to demonstrate the flexibility, efficiency and accuracy of the present method.",
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A Computational Scheme for the Interaction between an Edge Dislocation and an Arbitrarily Shaped Inhomogeneity via the Numerical Equivalent Inclusion Method. / Li, P.; Zhang, X.; Lyu, D.; Jin, X.; Keer, Leon M.

In: Physical Mesomechanics, Vol. 22, No. 2, 01.03.2019, p. 164-171.

Research output: Contribution to journalArticle

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T1 - A Computational Scheme for the Interaction between an Edge Dislocation and an Arbitrarily Shaped Inhomogeneity via the Numerical Equivalent Inclusion Method

AU - Li, P.

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AU - Jin, X.

AU - Keer, Leon M

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AB - The interactions between dislocations and inhomogeneity may play an important role in strengthening and hardening of materials. The problem can be solved analytically only for limited cases of simple geometry. By employing the recently developed numerical equivalent inclusion method, this work presents an effective computational scheme for studying the stress field due to an edge dislocation in the vicinity of an arbitrarily shaped inhomogeneity. The inhomogeneity is treated as an equivalent inclusion that is numerically discretized by rectangular elements. The mismatch between the matrix and the inhomogeneity materials are formulated through Dundurs’ parameters for numerical stability and robustness. The proposed method can efficiently and accurately evaluate the elastic field of the equivalent inclusion with the assistance of a fast Fourier transform based algorithm, constituting an essential refinement of the existing approach in the dislocation-inhomogeneity literature. Several benchmark examples are examined to demonstrate the flexibility, efficiency and accuracy of the present method.

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