Microcrack interaction with circular inclusion and interfacial zone

Abstract

A geometrically simplified plane elasticity problem of a finitesmall crack emanating from a thin interfacial zone surrounding the circularinclusion situated in the finite bounded domain is investigated. The crack isarbitrarily oriented and modelled using the distribution dislocation technique.This model represents the inner solution of the studied problem. Thecorresponding fundamental solution is based on the application ofMuskhelishvili complex potentials in the form of the Laurent series. Thecoefficients of the series are evaluated from the compatibility conditionsalong the interfaces of the inclusion, the interfacial zone and the enclosingmatrix. The fundamental solution is also used in the solution of the boundaryintegral method approximating the stress and strain relations of the so-calledouter solution. The asymptotic analysis at the point of the crack initiationcombines the inner and the outer solution and results in the evaluation of thestress intensity factors of the crack tip, which lies in the matrix. Thetopological derivative is subsequently used to approximate the energy releaserate field associated with the perturbing crack in the matrix. The extremevalues of the energy release rate allow one to assess the crack path directionof the initiated microcrack.A geometrically simplified plane elasticity problem of a finitesmall crack emanating from a thin interfacial zone surrounding the circularinclusion situated in the finite bounded domain is investigated. The crack isarbitrarily oriented and modelled using the distribution dislocation technique.This model represents the inner solution of the studied problem. Thecorresponding fundamental solution is based on the application ofMuskhelishvili complex potentials in the form of the Laurent series. Thecoefficients of the series are evaluated from the compatibility conditionsalong the interfaces of the inclusion, the interfacial zone and the enclosingmatrix. The fundamental solution is also used in the solution of the boundaryintegral method approximating the stress and strain relations of the so-calledouter solution. The asymptotic analysis at the point of the crack initiationcombines the inner and the outer solution and results in the evaluation of thestress intensity factors of the crack tip, which lies in the matrix. Thetopological derivative is subsequently used to approximate the energy releaserate field associated with the perturbing crack in the matrix. The extremevalues of the energy release rate allow one to assess the crack path directionof the initiated microcrack.