Mechanics and Mechanisms of Deformation and Microstructural Evolution
Personnel: S.B. Biner (PI) and J.R. Morris (PI)
Abstract:
The main objectives of this research effort are to develop (1) a fundamental
understanding of the hierarchy of scales of events that occur during the
deformation and failure processes of crystalline solids and (2) an improved
understanding of the underlying mechanisms for microstructural evolution
in the solid state that are driven by the spatially and temporally inhomogeneous
quantities spanning many different length and time scales. The ultimate objective
is the marriage of these two main objectives, so that deformation and solid-state
phase transformations (e.g., dynamic recrystalization and grain growth, nucleation
and growth of second phases) can be simulated in a seamless manner using
accurate parameters for the kinetics of the evolution.
Recent Results:
Current research efforts are concentrated on developing 2D and 3D dislocation
dynamics simulation algorithms in order to understand the cooperative behavior
of a very large number of dislocations, including their reactions, self-organization
and interactions with grain boundaries, point defects and second-phases at
the mesoscale.
We have recently studied the evolution of the flow stress for grain sizes ranging from about 16 to 2mm under shear deformation was simulated using two dimensional discrete dislocation dynamics.
Fig.1 Evolution of dislocation microstructures at 0.38% shear strain. Red and black colors show the dislocation dipoles. The simulation cell is 25 microns square.
The analyses were confined to a single slip system and to the collective behavior of a large number of edge dislocations, modeled as line defects in elastic medium. A superposition technique, combined with Boundary Element Method (BEM), was used to obtain the solution resulting from the dislocation microstructures and kinematic boundary conditions. The long-range interactions of dislocations were fully accounted for with the Multi-Pole Algorithm (MPA) without introducing an artificial cutoff radius. The various microstructures are shown in Fig. 1, where it seen that the smaller grain sizes result in more homogeneous deformation. The corresponding stress-strain curves for these systems are shown in Fig. 2. Flow stress values increased with decreasing grain size and correlated with grain size in the form of classical Hall-Petch [d]-1/2 relationship . However, a similar correlation was also observed between the flow stress and grain size in the form of [d]-1.
Fig.2 Left evolution of stress-strain curve for different grain sizes. Middle, correlation of flow stress with [d]-1/2 as classical Hall-Petch Relation and Right, correlation of flow stress with [d]-1.
The flow stress values for different grain sizes unified to a single curve when expressed as a function of the dislocation density normalized by the grain size. It was observed that dislocation pileups can both activate neighboring dislocation sources and also shutdown the active dislocation sources.
Significance:
Due to the efficiency of our 2D code (MPA combined with BEM), we are able
to study the self-organization and interaction behavior of a very large number
of dislocations (~10,000), calculating their interactions directly without
introducing any other artificial length scale. We note that a number of researchers
are currently pursuing 3D dislocation dynamics; however, relatively few researchers
are examining the collective behavior of large numbers of dislocations.
Future Work:
We are currently investigating the role that grain size distribution, multiple
slip planes, and grain boundary viscosity have on the grain boundary strengthening
behavior in 2D. Our studies on dislocation dynamics have been also extended
to 3D in collaboration with Prof. N. Ghoniem (UCLA). A superposition technique
is needed along with the dislocation dynamics in order to take into account
finite geometry effects (i.e., grain morphology, free surfaces and resulting
image forces on the dislocation loops) and kinematic boundary conditions..
Our studies on 2D simulations indicated that the most suitable approach is
to use of BEM. Accordingly, a 3D-BEM code has been developed which will be
incorporated into 3D Dislocation Dynamics.
Interactions:
We are in close collaboration with Prof. Ghoniem (UCLA) for the development
of a 3D dislocation dynamic simulation. We are also collaborating with Dr.
D. Wolf (ANL) for grain boundary mobility during creep and superplastic deformation
through the Computational Materials Science Network.
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Last update: February 19, 2008