Project Details
Projekt
Pinning and Relaxation of Dislocations in Continuum and Atomistic Models
Subject Area
Mathematics
Mechanics
Thermodynamics and Kinetics as well as Properties of Phases and Microstructure of Materials
Mechanics
Thermodynamics and Kinetics as well as Properties of Phases and Microstructure of Materials
Term
since 2020
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 441523275
Nucleation and glide of lattice dislocations is the most important mechanism of plastic deformation of ductile crystalline metals under external load. Studying dislocation motion is therefore of fundamental importance for understanding the mechanical strength of metals and alloys. Here, we propose to study some open problems of dislocation motion using both discrete atomistic and continuum approaches, of mutual benefit to both fields of modeling. On the continuum side, we will study line-tension based variational evolution of dislocations in heterogeneous environments. Interaction of dislocations with a heterogeneous environment leads to a stick-slip-behavior of the dislocation line. The mathematical interest now lies in the derivation of effective evolution models, which requires a description of the effective dislocation line tension. To this end, we will also consider relaxation problems. We will use full atomistic or mesoscopic (i.e., Peierls-Nabarro-type) models to construct energetically optimal microstructures on various length scales. It is an open question whether the microstructures derived from Peierls-Nabarro-type models can be observed in experiments. Such relaxation phenomena have not been studied using realistic atomistic models. We thus propose to use molecular dynamics simulation with realistic interaction potentials to study whether dislocation structures predicted from Peierls-Nabarro models can be stabilized. In order to be able to perform atomistic simulations on the length scales necessary to observe such mesoscopic relaxation phenomena, we will develop novel variational Green's function-based methods to provide exact elastic boundary conditions for atomistic simulation. Aside from classical materials we will also consider High Entropy Alloys (HEAs), a class of materials composed of usually five or more elements in high concentration. HEAs are interesting due to their potentially exceptional strength and hardness, wear resistance, and corrosion and oxidation resistance, among other desirable properties. From a modeling point of view, HEAs pose new challenges, as dislocations in these materials are immersed in a random spatially fluctuating environment. We will derive both novel mathematical tools as well as atomistic simulation approaches for stochastic homogenization of this random environment.
DFG Programme
Priority Programmes
