Modeling of Dislocation Structures in Materials

Dislocations play a key role in the understanding of many phenomena in solid state physics, materials science, crystallography and engineering. Dislocations are line defects producing distortions and self-stresses in an otherwise perfect crystal lattice. In particular, dislocations are the primary carrier of crystal plasticity and in dislocation based fracture mechanics.

Stressed dislocation pattern formation in crystal plasticity at finite deformation is demonstrated for the first time. Size effects are also demonstrated within the same mathematical model. The model involves two extra material parameters beyond the requirements of standard classical crystal plasticity theory. The dislocation microstructures shown are decoupled from deformation microstructures, and emerge without any consideration of latent hardening or constitutive assumptio...

An action functional is developed for nonlinear dislocation dynamics. This serves as a first step towards the application of effective field theory in physics to evaluate its potential in obtaining a macroscopic description of dislocation dynamics describing the plasticity of crystalline solids. Connections arise between the continuum mechanics and material science of defects in solids, effective field theory techniques in physics, and fracton tensor gauge theories. The sch...

It is shown that the dynamics of a two-dimensional crystal with a finite concentration of dislocations, as well as vacancy and interstitial defects, is governed by the hydrodynamic equations of a viscoelastic medium. At the longest length scales the viscoelasticity is described by the simplest Maxwell model, whose shear and compressional relaxation times are obtained in terms of microscopic quantities, including the density of free dislocations. At short length scales, bond o...

The dynamics and thermodynamics of dislocated crystals are studied within the framework of the nonlinear theory of elastic and plastic deformations.

In this work we investigate the theory of dynamics of dislocations in quasicrystals. We consider three models: the elastodynamic model of wave type, the elasto-hydrodynamic model, and the elastodynamic model of wave-telegraph type. Similarities and differences between the three models are pointed out and discussed. Using the framework of linear incompatible elastodynamic theory, the equations of motion of dislocations are deduced for these three models. Especially, the equati...

We review the continuous theory of dislocations from a mathematical point of view using mathematical tools, which were only partly available when the theory was developed several decades ago. We define a space of dislocation measures, which includes Hausdorff measures representing the dislocation measures of single dislocation curves. The evolution equation for dislocation measures is defined on this space. It is derived from four basic conditions, which must be satisfied by ...

We use the phase field crystal model to study nucleation of edge dislocations in two dimensions under an applied stress field. A dislocation dipole nucleates under the applied stress, consistent with Burgers vector conservation. The phase field correctly accounts for elastic energy storage prior to nucleation, and for dissipative relaxation during the nucleation event. We show that a lattice incompatibility field is a sensitive diagnostic of the location of the nucleation eve...

Plastic deformation, at all strain rates, is accommodated by the collective motion of crystalline defects known as dislocations. Here, we extend an analysis for the energetic stability of a straight dislocation, the so-called line tension ($\Gamma$), to steady-state moving dislocations within elastically anisotropic media. Upon simplification to isotropy, our model reduces to an explicit analytical form yielding insight into the behavior of $\Gamma$ with increasing velocity...

The phase-field crystal model in its amplitude equation approximation is shown to provide an accurate description of the deformation field in defected crystalline structures, as well as of dislocation motion. We analyze in detail the elastic distortion and stress regularization at a dislocation core and show how the Burgers vector density can be directly computed from the topological singularities of the phase-field amplitudes. Distortions arising from these amplitudes are th...