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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, Abstract
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[1]. 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)[2] 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[3]. 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
[1] Hills, D.A., Kelly, P.A., Dai, D.N., Korsunsky, A.M., 1996. Solution of Crack Problems:
The Distributed Dislocation Technique. Kluwer Academic Publishers. [2] 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, [3] Markenscoff, X., 1993. Interaction of dislocations and dislocation dipoles with cracks and anticracks, Mater. Sci. Forum 123-125, 525-530.