Discrete dislocation plasticity and crack tip fields in single crystals

Abstract

Discrete dislocation plasticity and crack tip fields in single crystals van der Giessen, E.; Deshpande, V.S.; Cleveringa, H.H.M.; Needleman, A. Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. AbstractSmall-scale yielding around a stationary plane strain mode I crack is analyzed using discrete dislocation plasticity. The dislocations are all of edge character, and are modeled as line singularities in a linear elastic material. Superposition is used to represent the solution in terms of analytical ÿelds for edge dislocations in a half-space and a numerical image solution that enforces the boundary conditions. The description of the dislocation dynamics includes the lattice resistance to dislocation motion, dislocation nucleation, interaction with obstacles and annihilation. A model planar crystal with three slip systems is considered. Two slip system orientations are analyzed that di er by a 90 • rotation. The non-hardening, single crystal plasticity continuum slip solution of Rice (Mech. Mater. 6 (1987) 317) for this model crystal predicts that slip and kink bands emerge for both crystal geometries, while Drugan (J. Mech. Phys. Solids 49 (2001) 2155) has obtained kink band free solutions. For a reference set of parameter values, kink band free solutions are found in one orientation while the emergence of kink bands is seen in the other orientation. However, lowering the dislocation source density suppresses the formation of kink bands in this orientation as well. In all calculations, the opening stress in the immediate vicinity of the crack tip is much larger than predicted by continuum slip theory. ?

A discrete dislocation analysis of near-threshold fatigue crack growth

“…Thus, continuum crystal plasticity predicts that the three slip system material is more effective in relaxing the near-tip stresses and hence would be expected to have a higher resistance to crack growth. It is worth mentioning here that away from the neartip region the stress levels in the discrete dislocation simulations of Van der Giessen et al [12] agree very well with the continuum plasticity values. Discrete dislocation predictions (with the irreversible cohesive law) of monotonic crack growth resistance curves for the two and three slip system materials are shown in Fig.…”

“…As in previous monotonic loading studies by Cleveringa et al [11] and Van der Giessen et al [12], full boundary value problem solutions are obtained for small-scale yielding of a mode I crack in plane strain. The loading is imposed by prescribing displacements corresponding to the isotropic, linear elastic mode I singular fields remote from the crack tip.…”

“…The boundary value problem formulation and the numerical implementation follow that in Refs. [11,12] where further details and additional references are given.…”

“…The loading is imposed by prescribing displacements corresponding to the isotropic, linear elastic mode I singular fields remote from the crack tip. The only difference from the problems in Refs [11,12] is that the remote stress intensity factor is taken to be a cyclic function of time varying between a specified K min and K max . Plane strain conditions are taken to prevail and the dislocations, which are represented as line singularities in an elastic solid, are all of edge character.…”

Micromechanics Simulations of Fracture

“…the effect of the discrete dislocation-induced stress field fluctuations on the crack growth process. The discussion is based on the discrete dislocation analyses by Cleveringa et al (18) and Van der Giessen et al (19) for mode I loading conditions.…”