Papers by Author: Roman Gröger

Abstract: Small prismatic dislocation loops in BCC metals have Burgers vectors either ½<111> or <100> and are usually close to circular shape. In atomistic simulations constructing prismatic dislocation loops of different shapes is straightforward, however, it is difficult to compare their formation energies, since loops of different shapes or different Burgers vectors do not necessarily have exactly the same size. Here we develop a general method to correctly compare loops of similar size but different shapes and the Burgers vectors. This method is combined with molecular statics simulations to identify the most energetically favorable shapes of prismatic dislocation loops in elastically isotropic tungsten and anisotropic α-iron.

Abstract: We develop a phase field model that describes the elastic distortion of a ferroelastic material with cubic anisotropy due to an arbitrary dislocation network and a uniform external load. The dislocation network is characterized using the Nye tensor and enters the formulation via a set of incompatibility constraints for the internal strain field. The long-range elastic response of the material is obtained by minimization of the free energy that accounts for higher order terms of the order parameters and symmetry-adapted strain gradients. To demonstrate the performance of the model, a minimal version of continuum dislocation dynamics is used to investigate the simultaneous evolution of the network of geometrically necessary dislocations and the internal strain field.

Abstract: We introduce a mesoscopic framework that is capable of simulating the evolution of dislocation networks and, at the same time, spatial variations of the stress, strain and displacement fields throughout the body. Within this model, dislocations are viewed as sources of incompatibility of strains. The free energy of a deformed solid is represented by the elastic strain energy that can be augmented by gradient terms to reproduce dispersive nature of acoustic phonons and thus set the length scale of the problem. The elastic strain field that is due to a known dislocation network is obtained by minimizing the strain energy subject to the corresponding field of incompatibility constraints. These stresses impose Peach-Koehler forces on all dislocations and thus drive the evolution of the dislocation network.

Abstract: The continuum theory of dislocations, as developed predominantly by Kröner and Kosevich, views each dislocation as a source of incompatibility of strains. We show that this concept can be employed efficiently in the Landau free energy functional to develop a mean-field mesoscopic model of materials with dislocations. The order parameters that represent the distortion of the parent phase (often of cubic symmetry) are written in terms of elastic strains which are themselves coupled by incompatibility constraints. Since the “strength” of the incompatibility depends on the local density of dislocations, the presence of dislocations affects the evolution of the microstructure and vice versa. An advantage of this formulation is that long range anisotropic interactions between dislocations appear naturally in the formulation of the free energy. Owing to the distortion of the crystal structure around dislocations, their presence in multiphase materials causes heterogeneous nucleation of the product phase and thus also shifts of the transformation temperature. This novel field-theoretical approach is very convenient as it allows to bridge the gap in studying the behavior of materials at the length and time scales that are not attainable by atomistic or macroscopic models.