Discrete Dislocation Predictions for Single Crystal Hardening: Tension VS Bending
Part of the
Solid Mechanics and Its Applications
book series (SMIA, volume 114)
Two boundary value problems are solved for a planar single crystal strip: tension and bending. Plastic flow arises from the motion of discrete dislocations, which are modeled as line defects in a linear elastic medium. Two sets of constitutive rules for sources and obstacles are used: (i) rules that only account for a static set of initial point sources and obstacles; (ii) rules that, in addition, account for the dynamic creation (and possible destruction) of dislocation junctions that can act as sources or obstacles. In tension, the overall stress-strain response is essentially ideally plastic when rule set (i) is employed while a two-stage hardening behavior, with a high hardening second stage, occurs when the number of sources and obstacles evolves dynamically. No major difference between the predictions of the two sets of constitutive rules is found in bending where the density of geometrically necessary dislocations dominates.
KeywordsConstitutive behavior dislocations metallic materials
A. A. Benzerga, Y. Bréchet, A. Needleman, and E. Van der Giessen. Incorporating 3D Mechanisms into 2D Dislocation Dynamics. in preparation.Google Scholar
J. F. Nye. Some geometrical relations in dislocated crystals. Acta metall.
, 1:153–162, 1953.CrossRefGoogle Scholar
M. F. Ashby. The deformation of plastically non-homogeneous materials. Phil. Mag.
, 21:399–424, 1970.CrossRefGoogle Scholar
E. Van der Giessen and A. Needleman. Discrete dislocation plasticity: a simple planar model. Modelling Simul. Mater Sci. Eng.
, 3:689–735, 1995.CrossRefGoogle Scholar
H. H. M. Cleveringa, E. Van der Giessen, and A. Needleman. A Discrete Dislocation Analysis of Bending. Int. J. Plasticity
, 15:837–868, 1999.CrossRefGoogle Scholar
A. A. Benzerga, S. S. Hong, K.-S. Kim, A. Needleman, and E. Van der Giessen. Smaller is Softer: A Discrete Dislocation Analysis of an Inverse Size Effect in a Cast Aluminum Alloy. Acta mater.
, 49:3071–3083,2001.CrossRefGoogle Scholar
G. Saada. Sur le durcissement dû à la recombinaison des dislocations. Acta metall.
, 8:841, 1960.CrossRefGoogle Scholar
V. B. Shenoy, R. V. Kukta, and R. Phillips. Mesoscopic Analysis of Structure and Strength of Dislocation Junctions in fcc Metals. Phys. Rev. Lett.
, 84:1491–1494,2000.CrossRefGoogle Scholar
A. J. E. Foreman. The Bowing of a Dislocation Segment. Phil. Mag.
, 15:1011–1021, 1967.CrossRefGoogle Scholar
A. Moulin, M. Condat, and L. R Kubin. Simulation of Frank—Read Sources in Silicon. Acta mater.
, 45:2339–2348, 1997.CrossRefGoogle Scholar
© Springer Science+Business Media Dordrecht 2004