Dislocation based Plasticity

P2 - A Novel Approach to the Problem of Dynamic Closure

 

Every Continuum Dislocation Dynamics theory must fulfill a number of criteria: (i) its field variables (e.g. densities) must be derived by well defined statistical averaging steps from systems of discrete dislocations; (ii) it must be kinematically and (iii) dynamically consistent.

"Kinematic consistency" describes the ability to evolve dislocations as curved lines together with the line length change during motion in a given velocity field. It thus considers only geometrical aspects of averaged dislocation systems of dislocations and the respective time evolution. "Dynamic consistency" is the ability to predict the evolution of dislocations under externally applied load as well as mutual interactions between dislocations. Our CDD theory was rigorously derived to solve the problem of kinematic consistency. The problem of dynamic consistency, however, is still far from being solved.

Thus, the goal of this project is the development of a self-consistent, physically based formulation of dislocation mobility functions: they connect dislocation velocities to the internal/external stress state and to dislocation field variables, their spatial derivatives as well as to properties of the underlying crystal lattice. Our novel approach consists in assembling an extensive database of local stress, velocity and dislocation microstructure data from large-scale DDD simulations. Statistical analysis of those dislocation structures and their evolution will then – in a data-driven approach – yield generic expressions that constitutively complete plasticity theories on the mesoscale and furthermore will guide towards understanding the collective behavior of dislocations.

  • dynamic closure: how do mesoscopic stresses relate to mesoscale density(-like) fields? find the functional form for

  • departing from commonly used phenomenological approximations that are tailored to highly specialized situations (cf. ‘forward problem’)

 

  • instead: data-driven research paradigm to parameterize generic non-linear functions based on data extracted from large-scale DDD simulations (the ‘inverse problem’)

Members :
Prof. Dr. Stefan Sandfeld, Institute: Institute of Mechanics and Fluid Dynamics, TU Bergakademie Freiberg
Prof. Dr. Nina Gunkelmann, Institute: Institute of Applied Mechanics, TU Claustal