| dc.description.abstract | Multi-scale simulation techniques are increasingly being applied to the study of engineering
problems, where characterizing phenomena occur at different length scales and where phenomena
occurring at some length scale influences phenomena occurring at a different length scale. In
material performance studies, it is understood that bonding at the atomic length scale, aggregation
of grains, the existence and evolution of defects, all contribute to material behaviour.
The goal of this research was to develop models that enabled the simulation at various length scales
intended to capture a metal’s behaviour, and to link these models to enable data transfer up the
length scales. The study was founded on the application of the embedded atom method (EAM) to
the iron (Fe) and iron carbide (Fe-C) lattices, and on the understanding that plasticity is primarily
driven by the motion of dislocations. The work involved the development of Fortran code for the
implementation of the EAM, the simulation of the stress fields for both static and dynamic
dislocation cores, the assembly of dislocation lines within slip planes, the assembly of slip planes
within a material’s lattice, and the implementation of grain evolution using finite element code. The
models at the lower length scales were validated using empirical and Ab-initio Peierl’s stress data.
The work was carried out in five stages corresponding to the length scales considered.
The lowest level length scale (dislocation core-length scale) was used to study the evolution of the
dislocation core. This was done by simulating the motion of dislocation core atoms in a lattice
containing a single dislocation line, under an externally applied load, and tracking the resulting
stress around the dislocation core. The principle result was the establishment of the link between the
Peierl’s stress and the smallest peak amplitude of the direct stress components for a dislocation line
in the [111�] direction. This work gave rise to the path of least resistance (POLR) method used to
predict the Peierls stress peak around the dislocation core. A mechanism for the motion of
dislocation core atoms was established and the POLR stresses for different dislocation types were
evaluated.
The line-length scale was used to characterize the effects of the dislocation core’s distortion
extended over a wider region than that possible within the capability of the EAM. This was done by
the simulation of the stress profile resulting from a dislocation line, with the peak POLR stress
This work gave rise to the misfit potential (MP) which enabled the determination of the longer
range dislocation stress field through which, interactions with other lattice defects would take place.
The results of the simulation of the behaviour of the interaction of dislocations dipoles are reported.
The plane-length scale accounted for the interaction of dislocation lines within the slip plane. The
theory of generalized functions (distributions) was applied to profile the spatial position of
interacting dislocations, and to relate them to the resulting stress amplitude profile. This work gave
rise to the plane structure factor (PSF), which was used to determine the planar dislocation density
which was used as an input at the next higher length scale. The model was used to determine the
resulting stress field over a slip plane containing assemblies of planar dislocation structures, and the
stress field was then used to predict the evolution of the dislocation assembly.
The structure-length scale accounted for the assembly of slip planes to construct 3-dimensional (3D)
dislocation structures. This stage accounted for the peak POLR stress and applied the misfit
potential in the study of 2-dimensional (2-D) dislocation lines assembled into a 3-D dislocation
structure. Simulations were carried out to determine the resulting stress field, which was used to
characterize a 3-D dislocation structure factor. This work gave rise to the network structure factor
(NSF), which was used to determine the network dislocation density which was used as an input at
the next higher length scale. The model was used to determine the resulting stress field in a lattice
containing dislocation structures.
The network structure factor was then used as an input into a finite element formulation that was
used at the meso-length scale. This factor captured the mechanistic events at the underlying l
incorporate the physics of the material’s behaviour in the prediction of its deformation. The outputs
of this research are the POLR model, the MP model, the PSF model, the NSF model, the meso-scale
model, the linkages between these models, the linking of these models with Peierls stress data and
dislocation density data, and the link to grain size driven yield stresses of materials. These results
are expected to complement current and future work in materials characterization and alloy
development, and enhance the value of simulation in engineering design | en_US |
