Modeling microbending of thin films through discrete dislocation dynamics, continuum dislocation theory, and gradient plasticity

Constitutive models that describe crystal microplasticity in a continuum framework can be envisaged as average representations of the dynamics of dislocation systems. Thus, their performance needs to be assessed not only by their ability to correctly represent stress-strain characteristics on the specimen scale but also by their ability to correctly represent the evolution of internal stress and strain patterns. Three-dimensional discrete dislocation dynamics (3D DDD) simulations provide complete knowledge of this evolution, and averages over ensembles of statistically equivalent simulations can therefore be used to assess the performance of continuum models. In this study, we consider the bending of a free-standing thin film. From a continuum mechanics point of view, this is a one-dimensional (1D) problem as stress and strain fields vary only in one dimension. From a dislocation plasticity point of view, on the other hand, the spatial degrees of freedom associated with the bending and piling up of dislocations are essential. We compare the results of 3D DDD simulations with those obtained from a simple 1D gradient plasticity model and a more complex dislocation-based continuum model. Both models correctly reproduce the nontrivial strain patterns predicted by 3D DDD for the microbending problem.