Dislocation model of an asymmetric weak zone for problems of interaction between crack-like defects

Abstract

An adhesively bonded asymmetric weak zone is proposed as a model for studying the problem of interaction between crack-like defects in an elastic medium. The opening of the weak zone is prescribed by a two-parameter basis function, i.e. by a special dislocation which automatically accounts for the asymmetry and other expected physical features of the stress–strain field near the tips of the weak zone. The adhesive forces corresponding to the prescribed opening are then calculated from the solution of the particular problem. The application of the model is demonstrated on the problem of a long interface crack subjected to wedge opening forces which is separated from a short collinear interface weak zone by a small unbroken strong microstructural feature (a small obstacle). Two key questions pertaining to limiting situations are addressed: (i) when does the weak zone become the nucleus of a cohesive crack on its own without linking with the pre-existing long crack; and (ii) when does it force the rupture of the obstacle and coalesce with the long crack.

Acknowledgements

This work was partly supported by a grant to IVS under the Program of the Russian Academy of Sciences ‘Structural Mechanics of Materials and Structures. Interaction of Nano–Micro–Meso–Macro Scales’.

Notes

On leave from The Institute of Problems of Mechanics, Russian Academy of Sciences, Moscow, Russia.

Additional information

Notes on contributors

B. L. Karihaloo *

On leave from The Institute of Problems of Mechanics, Russian Academy of Sciences, Moscow, Russia.