<p>We study the plane strain problem associated with two circular compressible liquid inclusions embedded in an infinite isotropic elastic matrix subjected to the action of an edge dislocation located at an arbitrary position. With the aid of the techniques of conformal mapping and analytic continuation, the boundary value problem is ultimately reduced to an infinite system of linear algebraic equations, which, when solved via truncation leads to the elastic field in the matrix and the internal uniform hydrostatic stress fields within the two circular liquid inclusions. In addition, an explicit expression for the image force acting on the edge dislocation is derived using the Peach-Koehler formula. Numerical results are presented to demonstrate the effect of the two liquid inclusions on the mobility and stability of the edge dislocation. The stiffening and hardening effect of the two liquid inclusions can be observed under certain circumstances.</p>

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An edge dislocation interacting with two circular compressible liquid inclusions

  • Xu Wang,
  • Peter Schiavone

摘要

We study the plane strain problem associated with two circular compressible liquid inclusions embedded in an infinite isotropic elastic matrix subjected to the action of an edge dislocation located at an arbitrary position. With the aid of the techniques of conformal mapping and analytic continuation, the boundary value problem is ultimately reduced to an infinite system of linear algebraic equations, which, when solved via truncation leads to the elastic field in the matrix and the internal uniform hydrostatic stress fields within the two circular liquid inclusions. In addition, an explicit expression for the image force acting on the edge dislocation is derived using the Peach-Koehler formula. Numerical results are presented to demonstrate the effect of the two liquid inclusions on the mobility and stability of the edge dislocation. The stiffening and hardening effect of the two liquid inclusions can be observed under certain circumstances.