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Interaction of cracks with dislocations and dislocation dipoles
in couple-stress elasticity
K.P. Baxevanakis1, P.A. Gourgiotis2, H.G. Georgiadis3
1Mechanics Division, National Technical University of Athens, Zographou Campus, Zographou, GR-15773,
2Department of Mechanical and Structural Engineering, University of Trento, Trento, I-38123, Italy;
3Mechanics Division, National Technical University of Athens, Zographou Campus, Zographou, GR-15773,
The interaction between cracks and dislocations is a fundamental problem of fracture
mechanics, since this interaction determines, in many cases, the macroscopic brittle or ductile
material response. In the present work, we study the interaction of a single crack with a single
dislocation or a dislocation dipole within the framework of the generalized continuum theory
of couple-stress elasticity. The standard couple-stress theory (with no independent rotation) is
the simplest theory of elasticity in which couple-stresses arise.
Our approach is based on the distributed dislocation technique. The cracks are modeled
either by a continuous distribution of dislocations or by a continuous distribution or
infinitesimal dislocation dipoles. In the case of the interaction of a crack with a climb
dislocation, rotational defects have to be distributed as well (constrained wedge
disclinations) to satisfy the boundary conditions along the crack faces. The final results are
obtained by numerically solving a system of coupled singular or hypersingular integral
equations. The interaction of a crack with a glide or a screw dislocation is governed by a
single singular or a single hypersingular integral equation.
The results for the near-tip fields differ in several respects from the predictions of the
classical fracture mechanics. In particular, the present results indicate that a cracked solid
governed by couple-stress elasticity behaves in a more rigid way (having increased stiffness)
as compared to a solid governed by classical elasticity. Also, the stress level at the crack-tip
region is appreciably higher, within a small zone adjacent to the tip, than the one predicted by
classical elasticity while the crack-face displacements and rotations are significantly smaller
that the respective ones in classical elasticity. In all cases the J
-integrals in both crack tips and
the configurational (Peach-Koehler) forces on the defects are calculated.
 Hills, D.A., Kelly, P.A., Dai, D.N., Korsunsky, A.M., 1996. Solution of Crack Problems:
The Distributed Dislocation Technique. Kluwer Academic Publishers.
 Gourgiotis, P.A., Georgiadis H.G., 2008. An approach based on distributed dislocations
and disclinations for crack problems in couple-stress elasticity, Int. J. Solids Struct. 45,
 Markenscoff, X., 1993. Interaction of dislocations and dislocation dipoles with cracks and
anticracks, Mater. Sci. Forum 123-125, 525-530.
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