Mc. Fivel et al., IMPLEMENTING IMAGE STRESSES IN A 3D DISLOCATION SIMULATION, Modelling and simulation in materials science and engineering, 4(6), 1996, pp. 581-596
A three-dimensional (3D) dislocation simulation has been developed in
the last few years in order to fill the gap between atomistic simulati
ons and the more macroscopic approaches. The specific role of such a s
imulation is to combine all mechanisms responsible for the hardening (
e.g. the forest mechanism) and the multiplication of dislocations whic
h typically occur in three dimensions. Many problems involve the prese
nce of interfaces, which can come from cracks, oxide layers, particles
etc. The present work deals with a method to tackle such problems in
a 3D simulation. It is firstly restricted to the image stress case. A
method of calculating the image stress field of dislocation segments d
ue to the presence of a semi-infinite free surface has been proposed b
y Gosling and Willis. An alternative method is proposed here based on
the Boussinesq problem of point loading in a half-space. It is firstly
shown on simple cases that the methods are equivalent. The latter one
is used in the present simulation, and the image stress field due to
populations of dislocations is investigated. From a practical point of
view, we calculate the depths within which all dislocations have to b
e taken into account, in order to get reasonable accuracy on the image
stresses, and we also investigate how this stress field decays in spa
ce.