Unified Framework for Dislocation-Based Defect Energetics

A variational approach is presented to calculate the stress field generated by a system of dislocations. It is shown that in the simplest case, when the material containing the dislocations obeys Hooke's law the variational framework gives the same field equations as Kr\"oner's theory. However, the variational method proposed allows to study many other problems like dislocation core regularisation, role of elastic anharmonicity and dislocation--solute atom interaction. The ai...

A detailed theoretical and numerical investigation of the infinitesimal single-crystal gradient plasticity and grain-boundary theory of Gurtin (2008) "A theory of grain boundaries that accounts automatically for grain misorientation and grain-boundary orientation". Journal of the Mechanics and Physics of Solids 56 (2), 640-662, is performed. The governing equations and flow laws are recast in variational form. The associated incremental problem is formulated in minimization f...

We develop a continuum model for the dynamics of grain boundaries in three dimensions that incorporates the motion and reaction of the constituent dislocations. The continuum model is based on a simple representation of densities of curved dislocations on the grain boundary. Illposedness due to nonconvexity of the total energy is fixed by a numerical treatment based on a projection method that maintains the connectivity of the constituent dislocations. An efficient simulation...

We formulate the laws governing the dynamics of a crystalline solid in which a continuous distribution of dislocations is present. Our formulation is based on new differential geometric concepts, which in particular relate to Lie groups. We then consider the static case, which describes crystalline bodies in equilibrium in free space. The mathematical problem in this case is the free minimization of an energy integral, and the associated Euler-Lagrange equations constitute a ...

A rigorous methodology is developed for computing elastic fields generated by experimentally observed defect structures within grains in a polycrystal that has undergone tensile extension. An example application is made using a near-field High Energy X-ray Diffraction Microscope measurement of a zirconium sample that underwent $13.6\%$ tensile extension from an initially well-annealed state. (Sub)grain boundary features are identified with apparent disclination line defects i...

Recent experiments, atomistic simulations, and theoretical predictions have identified various new types of grain boundary motions that are controlled by the dynamics of underlying microstructure of line defects (dislocations or disconnections), to which the classical motion by mean curvature model does not apply. Different continuum models have been developed by upscaling from discrete line defect dynamics models under different settings (dislocations or disconnections, low ...

Determining the positions of lattice defects on elastic surfaces with Gaussian curvature is a non-trivial task of mechanical energy optimization, particularly for surfaces with boundaries. We introduce a simple way to predict the onset of disclination disorder from the shape of bounded surfaces. The criterion fixes the value of a weighted integral Gaussian curvature to a universal constant and proves accurate across a great variety of shapes, even when previously suggested cr...

A description of dislocations and disclinations defects in terms of Riemann--Cartan geometry is given, with the curvature and torsion tensors being interpreted as the surface densities of the Frank and Burgers vectors, respectively. A new free energy expression describing the static distribution of defects is presented, and equations of nonlinear elasticity theory are used to specify the coordinate system. Application of the Lorentz gauge leads to equations for the principal ...

A phenomenological model of the evolution of an ensemble of interacting dislocations in an isotropic elastic medium is formulated. The line-defect microstructure is described in terms of a spatially coarse-grained order parameter, the dislocation density tensor. The tensor field satisfies a conservation law that derives from the conservation of Burgers vector. Dislocation motion is entirely dissipative and is assumed to be locally driven by the minimization of plastic free en...

Damage nucleation from repeated dislocation absorption at a grain boundary is simulated with molecular dynamics. At the grain boundary-dislocation intersection site, atomic shuffling events determine how the free volume brought by the incoming dislocation is accommodated. This process in turn determines the crack nucleation mechanism, as well as the critical strain and number of dislocations that can be absorbed before cracking. Slower strain rates promote earlier crack nucle...