A discrete dislocation analysis of residual stresses in a composite material

Citation
Hhm. Cleveringa et al., A discrete dislocation analysis of residual stresses in a composite material, PHIL MAG A, 79(4), 1999, pp. 893-920
Citations number
32
Categorie Soggetti
Apllied Physucs/Condensed Matter/Materiales Science
Journal title
PHILOSOPHICAL MAGAZINE A-PHYSICS OF CONDENSED MATTER STRUCTURE DEFECTS ANDMECHANICAL PROPERTIES
ISSN journal
13642804 → ACNP
Volume
79
Issue
4
Year of publication
1999
Pages
893 - 920
Database
ISI
SICI code
1364-2804(199904)79:4<893:ADDAOR>2.0.ZU;2-A
Abstract
Residual stresses and strains in a two-dimensional model composite consisti ng of elastic reinforcements in a crystalline matrix are analysed. The comp osite is subject to macroscopic shear and then unloaded. Plane-strain condi tions and single slip on slip planes parallel to the shear direction are as sumed. The dislocations are modelled as line defects in a linear elastic me dium. At each stage of loading, superposition is used to represent the solu tion in terms of the infinite medium solution for the discrete dislocations and an image solution that enforces the boundary conditions, which is non- singular and obtained from a linear elastic finite-element solution. The la ttice resistance to dislocation motion, dislocation nucleation and dislocat ion annihilation are incorporated into the formulation through a set of con stitutive rules. Obstacles leading to possible dislocation pile-ups are als o accounted for. Considerable reverse plasticity is found when the reinforc ement arrangement is such that all slip planes are cut by particles and whe n the unloading rate is equal to the loading rate. When unloading takes pla ce at a very high rate, the unloading slope is essentially elastic but rela xation of the dislocation structure occurs in the unloaded state. Predictio ns of the discrete dislocation formulation for residual stresses, residual strains and the strain variance are compared with corresponding predictions obtained using conventional continuum slip crystal plasticity. The effect of particle size, as predicted by the discrete dislocation description, is also addressed.