A displacement-based formulation for interaction problems between cracks and dislocation dipoles in couple-stress elasticity. (1st March 2019)

• Record Type: Journal Article
• Authors: Baxevanakis, K.P.; Georgiadis, H.G.
• Is Part Of: International journal of solids and structures. Volume 159(2019)
• Page Start: 1
• Page End: 20
• Publication Date: 2019-03-01
• Subjects: Cracks -- Dislocations -- Dislocation dipole -- Disclinations -- Microstructure -- Couple-stress elasticity -- Hyper-singular integral equations -- Distributed dislocation technique -- Peach-Koehler force; Mechanics, Applied -- Periodicals; Structural analysis (Engineering) -- Periodicals; Elastic solids -- Periodicals; Mécanique appliquée -- Périodiques; Constructions, Théorie des -- Périodiques; Solides élastiques -- Périodiques; Elastic solids; Mechanics, Applied; Structural analysis (Engineering); Periodicals; 624.18
• DOI: 10.1016/j.ijsolstr.2018.09.015
• Languages: English
• ISSNs: 0020-7683

Abstract

Abstract: Interaction problems of a finite-length crack with plane and antiplane dislocation dipoles in the context of couple-stress elasticity are presented in this study. The analysis is based on the distributed dislocation technique where infinitesimal dislocation dipoles are used as strain nuclei. The stress fields of these area defects are provided for the first time in the framework of couple-stress elasticity theory. In addition, a new rotational defect is introduced to satisfy the boundary conditions of the opening mode problem. This formulation leads to displacement-based hyper-singular integral equations that govern the crack problems, which are solved numerically. It is further shown that this method has several advantages over the slope formulation. Based on the obtained results, it is deduced that in all cases the cracked body behaves in a more rigid way when couple-stresses are considered. The effect of couple-stresses is highlighted in a small zone ahead of the crack-tip and around the dislocation dipole, where the stress level is significantly higher than the classical elasticity prediction. Further, the dependence of the energy release rate and the configurational force exerted on the defect on the characteristic material length and the distance between the defect and the crack-tip is discussed. In the plane problems, couple-stress theory predicts either strengthening or weakening effects while in the antiplane mode a strengthening effect is predicted.