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.