Interaction between an edge dislocation and a circular incompressible liquid inclusion

We use Muskhelishvili's complex variable formulation to study the interaction problem associated with a circular incompressible liquid inclusion embedded in an infinite isotropic elastic matrix subjected to the action of an edge dislocation at an arbitrary position. A closed-form solution to the problem is derived largely with the aid of analytic continuation. We obtain, in explicit form, expressions for the internal uniform hydrostatic stresses, nonuniform strains and nonuniform rigid body rotation within the liquid inclusion; the hoop stress along the liquid-solid interface on the matrix side and the image force acting on the edge dislocation. We observe that (1) the internal strains and rigid body rotation within the liquid inclusion are independent of the elastic property of the matrix; (2) the internal hydrostatic stress field within the liquid inclusion is unaffected by Poisson's ratio of the matrix and is proportional to the shear modulus of the matrix; and (3) an unstable equilibrium position always exists for a climbing dislocation.

Automated summary

In this study, Muskhelishvili's complex variable formulation was used to investigate the interaction problem of a circular incompressible liquid inclusion embedded in an infinite isotropic elastic matrix subjected to an edge dislocation. A closed-form solution to the problem was derived with the help of analytic continuation. The study obtained explicit expressions for internal uniform hydrostatic stresses, nonuniform strains, and nonuniform rigid body rotation within the liquid inclusion, as well as the hoop stress along the liquid-solid interface on the matrix side and the image force acting on the edge dislocation. It was observed that the internal strains and rigid body rotation within the liquid inclusion are independent of the elastic property of the matrix, the internal hydrostatic stress field within the liquid inclusion is unaffected by the matrix's Poisson's ratio and is proportional to the matrix's shear modulus, and an unstable equilibrium position always exists for a climbing dislocation.