E. Vandergiessen et A. Needleman, DISCRETE DISLOCATION PLASTICITY - A SIMPLE PLANAR MODEL, Modelling and simulation in materials science and engineering, 3(5), 1995, pp. 689-735
A method for solving small-strain plasticity problems with plastic flo
w represented by the collective motion of a large number of discrete d
islocations is presented. The dislocations are modelled as line defect
s in a linear elastic medium. At each instant, superposition is used t
o represent the solution in terms of the infinite-medium solution for
the discrete dislocations and a complementary solution that enforces t
he boundary conditions on the finite body. The complementary solution
is nonsingular and is obtained from a finite-element solution of a lin
ear elastic boundary value problem. The lattice resistance to dislocat
ion motion, dislocation nucleation and annihilation are incorporated i
nto the formulation through a set of constitutive rules. Obstacles lea
ding to possible dislocation pile-ups are also accounted for. The defo
rmation history is calculated in a linear incremental manner. Plane-st
rain boundary value problems are solved for a solid having edge disloc
ations on parallel slip planes. Monophase and composite materials subj
ect to simple shear parallel to the slip plane are analysed. Typically
, a peak in the shear stress versus shear strain curve is found, after
which the stress falls to a plateau at which the material deforms ste
adily. The plateau is associated with the localization of dislocation
activity on more or less isolated systems. The results for composite m
aterials are compared with solutions for a phenomenological continuum
slip characterization of plastic Row.