Influence of Dislocations on the Spatial Variation of Microstructure in Martensites

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.

Application of a 3D-Continuum Theory of Dislocations to a Problems of Constrained Plastic Flow: Microbending of a Thin Film

The advancing miniaturisation of e.g. microelectronic devices leads to an increasing interest in physically motivated continuum theories of plasticity in small volumes. Such theories need to be based on the averaged dynamics of dislocations. Preserving the line-like character of these defects, however, posed serious problems for the development of dislocation-based continuum theories, while continuum theories based on scalar dislocation densities necessarily stay on a phenomenological level. Within this work we apply a dislocation-based continuum theory, which is based on a physically meaningful averaging of dislocation lines, to the benchmark problem of bending of a free-standing thin film.