Method of Images Solution for an Edge Dislocation and a Circular Cavity in Crystalline Solids

K. Nguyen, A. Mehrabian

Research output: Contribution to journalArticlepeer-review

Abstract

Abstract: Mechanics of defects in solids across awide span of length scales is commonly formulated using thedislocations theory. This paper revisits the classical problemof interaction between an elastic edge dislocation and acircular cavity. A heuristic, yet, mechanistic approach is takento obtain the stress solution to this problem. The approach usescomplex variable theory of elasticity, along with method ofimages. For this purpose, a definition and formulation ofelastic dipole singularities similar to dipole charges inelectrostatics is developed. It is shown that an imagedislocation with Burger’s vector of the same strength as thereal dislocation but in opposite direction, as well as a set offour singularities including a dislocation dipole, amoment-dilatation dipole, and two centers of dilatation wouldestablish a circular, traction-free boundary in an infiniteelastic medium. Adding a Volterra dislocation to thefinite-length edge dislocation from this study would recover therelated problem of interaction between an infinite-length edgedislocation and circular cavity. The interesting analogy betweenthe considered elastic problem and the electrostatic problem ofinteraction between a line electric charge and a cylindricalconductor is discussed.

Original languageEnglish (US)
Pages (from-to)20-31
Number of pages12
JournalPhysical Mesomechanics
Volume24
Issue number1
DOIs
StatePublished - Jan 2021

All Science Journal Classification (ASJC) codes

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

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