Comparison of discrete dislocation and continuum plasticity predictions for a composite material Cleveringa, H.H.M.; van der Giessen, E.; 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. Download date: 11-04-2019Acfcr maf~r. Vol. 45, No. 8, pp. 3163.-3179, 1997 G (Received 8 October 1996; accepted 18 December 1996) Abstract-A two-dimensional model composite with elastic reinforcements in a crystalline matrix subject to macroscopic shear is analyzed using both discrete dislocation plasticity and conventional continuum slip crystal plasticity. In the discrete dislocation formulation, the dislocations are modeled as line defects in a linear elastic medium. At each stage of loading, superposition is used to represent the solution in terms of the infinite medium solution for the discrete dislocations and a complimentary solution that enforces the boundary conditions, which is non-singular and obtained from a linear elastic, finite element solution. The lattice resistance to dislocation motion, dislocation nucleation, and dislocation annihilation are incorporated into the formulation through a set of constitutive rules. Obstacles leading to possible dislocation pile-ups are also accounted for. Results are presented for materials with a single slip system. A reinforcement size effect is exhibited by the discrete dislocation-based analysis whereas the continuum slip results are size independent. The discrete dislocation results have higher average reinforcement stress levels than do the corresponding continuum slip calculations. Averaging of stress fields over windows of increasing size is used to gain insight into the transition from discrete dislocation-controlled to continuum behavior. IQ 1997 Acta Metallurgica Inc.1997 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rrghts reserved Printed in Great Britain PII: S1359-6454(97)00011-6 1359
A discrete dislocation analysis of mode I crack growth Cleveringa, H.H.M.; van der Giessen, E.; 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 plane strain mode I crack is analyzed using discrete dislocation dynamics. The dislocations are all of edge character, and are modeled as line singularities in an elastic material. At each stage of loading, superposition is used to represent the solution in terms of solutions for edge dislocations in a half-space and a complementary solution that enforces the boundary conditions. The latter is non-singular and obtained from a ®nite element solution. The lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation are incorporated into the formulation through a set of constitutive rules. A relation between the opening traction and the displacement jump across a cohesive surface ahead of the initial crack tip is also speci®ed, so that crack growth emerges naturally from the boundary value problem solution. Material parameters representative of aluminum are employed. For a low density of dislocation sources, crack growth takes place in a brittle manner; for a low density of obstacles, the crack blunts continuously and does not grow. In the intermediate regime, the average near-tip stress ®elds are in qualitative accord with those predicted by classical continuum crystal plasticity, but with the local stress concentrations from discrete dislocations leading to opening stresses of the magnitude of the cohesive strength. The crack growth history is strongly aected by the dislocation activity in the vicinity of the growing crack tip. #
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. ?
Plastic deformation in two-dimensionalmonophase and composite materials is studied using a discrete dislocation dynamics method. In this method, dislocations are represented by line defects in a linear elastic medium, and their interactions with boundaries or second-phase elastic particles are incorporated through a complementary finite element solution. The formulation includes a set of simple constitutive rules to model the lattice resistance to dislocation glide, as well as the generation, annihilation and pinning of dislocations at point obstacles. The focus is on the predicted strain hardening of these materials when only a single slip system is active. When the particle morphology is such as to require geometrically necessary dislocations, hardening in the composite materials exhibits a distinct size effect. This size effect is weaker than that predicted by simple analytical estimates based on geometrically necessary dislocations.
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