Abstract
A geometrically simplified plane elasticity problem of a finite small crack emanating from a thin interfacial zone surrounding the circular inclusion situated in the finite bounded domain is investigated. The crack is arbitrarily oriented and modelled using the distribution dislocation technique. This model represents the inner solution of the studied problem. The corresponding fundamental solution is based on the application of Muskhelishvili complex potentials in the form of the Laurent series. The coefficients of the series are evaluated from the compatibility conditions along the interfaces of the inclusion, the interfacial zone and the enclosing matrix. The fundamental solution is also used in the solution of the boundary integral method approximating the stress and strain relations of the so-called outer solution. The asymptotic analysis at the point of the crack initiation combines the inner and the outer solution and results in the evaluation of the stress intensity factors of the crack tip, which lies in the matrix. The topological derivative is subsequently used to approximate the energy release rate field associated with the perturbing crack in the matrix. The extreme values of the energy release rate allow one to assess the crack path direction of the initiated microcrack.
Highlights
M icrocracking is a phenomenon appearing in the vicinity of some stress rising features, where relatively short cracks rise and grow
The energy momentum tensor [7], [8] and the approximation of the energy release rate for any crack size and orientation by means of a topological derivative can be evaluated from the inner solution and the corresponding stress intensity factors at the crack tip lying in the matrix
The graph shows that for some combination of the external stresses T1 getting some specific value from the range T1 Î(-80,60) MPa it is difficult to assess the crack path direction, because the dependence of the energy release rate Ge is rather flat without the clear local extremal value
Summary
M icrocracking is a phenomenon appearing in the vicinity of some stress rising features, where relatively short cracks rise and grow. Crack path assessment; Complex potentials; Interfacial zone; Circular inclusion; Fundamental solution; Topological derivative.
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