Cisterna di Latina, Italy, 17 – 21 March 2014
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.
References  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.
Tetrabenazine Tablets Tetrabenazine Tablets are not addictive. Consumer Medicine Information What is in this leaflet Before you take Tetrabenazine It does not contain all of the available When you must not take it Do not take Tetrabenazine Tablets • You are allergic to tetrabenazine or against the benefits they expect it will If you have any concerns about
Trends and Outcomes in the Australian Pharmaceutical Benefits Scheme Kim Sweeny Pharmaceutical Industry Project Working Paper Series PO Box 14428 Melbourne VIC 8001 AUSTRALIA Trends and Outcomes in the Australian Pharmaceutical Benefits Scheme Kim Sweeny 1. Introduction The cost of the Pharmaceutical Benefits Scheme (PBS) to the Government has been the subj