An intrinsic discrete dislocation-finite element formulation of metal plasticity
Abstract
This work was carried out to develop and test a finite element based technique Lilat
incorporates dislocation information for use in simulating elastic and plastic behavior in Body
Centered Cubic metals and alloys.
Initial work focused on the development of energy balance equations incorporating dislocanou
interaction ana evolution components. Applying vananonal techruques, these equations were
combined giving rise to a governing equation amenable to finite element techniques. A
dislocation density field function was then developed and algorithms that enabled the
manipulation of the field according to material constitutive relations selected. Dislocation
density shape functions were developed and incorporated into a 3 dimensional finite element
formulation giving rise to a finite element technique incorporating intrinsic dislocation
information. The technique was validated by simulating loading over the elastic range and the
immediate region beyond yield of thin steel strips and comparing the results to those obtained
by conventional analysis. The method developed differed from standard and multi-scale discrete dislocation techniques
which require the definition of micro elements that capture the dislocation information which
are then assembled onto an elastic matrix in a two stage simulation process. The proposed
method instead focused on the development of a dislocation density field function and finite
element shape functions that incorporated the dislocation information into regular finite
elements paving the way for a one stage mechanistic simulation. This resulted in a simulation
process with a lower number of simulation cycles, which reduced simulation times and costs.
The work managed the task of incorporating data on the large volume of discrete dislocations
by the use of dislocation density in a black box technique. This eliminated the need to track
each discrete dislocation, and left the simulation with the task of monitoring the evolution of Lhedislocation densities. The simulation was also faced with the challenge of monitoring the
evolution of various families of dislocations. This was achieved by developing separate
algorithms that manipulated the density of each dislocation family along the loading path. The
work identified the slip planes as the regions within which the evolving dislocation families
contribute to plasticity and incorporated vector shape functions for 2 dimensional structures to
enable separation and hence tracking of the contribution of each active slip plane towards
strain accumulation. The work eventually incorporated the dislocation density information into
a continuum finite element framework using dislocation density shape functions. This enabled
a single stage simulation into the elastic and plastic range of material behavior. The work
combined a micro scale and a macro scale window of resolution of material behavior. To
integrate the two length scales the simulation incorporated meso-scale periodic elements that
aggregated the micro scale into the macro scale. Stress-strain curves, dislocation density field function, dislocation density shape functions and
slip plane percentage contribution factors were generated. Specifically the stress strain curves
generated upheld Hooke' law and demonstrated a definite yield plateau followed by material
recovery after yielding. The model however did not predict post yield hardening and fracture.
This work resulted in a finite element technique that may be used in simulation studies of
material degradation based upon mechanistic, micro structural evaluation and may enable
researchers and engineers work outside the limitations of existing material models and instead
base their evaluations upon an understanding of a materials microstructure as obtained from
non-destructive studies. The work also resulted in a sound platform upon which further
development of mechanistic based simulation may be initiated.
Sponsorhip
University of NairobiPublisher
Department of Civil Engineering, University of Nairobi