Statistics of Internal Elastic Fields of 3D Dislocations Systems

Statistics of Internal Elastic Fields of 3D Dislocations Systems: Computational Modeling and
Comparison with X-ray Measurements
Anter A. El-Azab, Associate Professor
Department of Scientific Computing, College of Arts and Sciences
Materials Science Program
Florida State University
Dirac Science Library
Tallahassee, FL 32306-4120
I will present a theoretical formulation and a simulation technique for the statistics of internal
elastic field of 3D dislocation systems in deforming crystals. The dislocation realizations are
generated by the method of dislocation dynamics simulation and their internal elastic fields in
the simulation volume is computed using an exact formulation of the stress boundary value
problem. Since the internal elastic fields of dislocations are highly fluctuating within the
crystal volume under consideration, we use probability density functions as well as pair
correlation functions to model their statistics. These statistical measures are established as
first and second order ensemble averages of internal stress with respect to a generalized
probability distribution function of dislocations. The statistical properties of the internal
stress, elastic strain, lattice rotation, lattice curvature tensor and dislocation density tensor in
dislocated crystals will be presented. A comparison with submicron resolved X-ray
measurements of lattice rotation and dislocation density tensor will be shown.