In the current paper we modify the evolution equations of the simplified continuum dislocation dynamics theory presented in [T. Hochrainer, S. Sandfeld, M. Zaiser, P. Gumbsch, Continuum dislocation dynamics: Towards a physical theory of crystal plasticity. J. Mech. Phys. Solids. (in print)] to account for the nature of the so-called curvature density as a conserved quantity. The derived evolution equations define a dislocation flux based crystal plasticity law, which we present in a fully three-dimensional form. Because the total curvature is a conserved quantity in the theory the time integration of the equations benefit from using conservative numerical schemes. We present a discontinuous Galerkin implementation for integrating the time evolution of the dislocation state and show that this allows simulating the evolution of a single dislocation loop as well as of a distributed loop density on different slip systems.

A generic model of bulk crystal plasticity with stochastic evolution of the local microstructure is formulated. The evolution of local fluctuations of internal stress and plastic strain, as well as the cross correlation between these variables, is investigated for different loading modes (stress control vs. displacement control) as a function of the coarse graining scale, and the spatial structure of the respective correlation functions is determined. The investigations demonstrate that, after an initial transient characterized by uncorrelated initiation of plasticity in different sample locations, nontrivial long range correlations emerge both within the strain pattern and between the internal stress and plastic strain patterns. The internal stresses, on the other hand, remain short range correlated throughout. Implications of our findings for larger-scale plasticity models are discussed.

The plasticity of micro-pillar deformation has widely been studied by discrete dislocation dynamics simulations to explain the so-called size effect. In this study the role of glissile junctions forming during plastic deformation under various loading scenarios is in the center of interest. The activity of these naturally forming dislocation sources is followed in detail. Surprisingly these junctions are rather active sources and not just another obstacle as often assumed. Their relative contribution to the overall dislocation density for the simulated specimens reaches often values of 20% or even more. The formation of such a glissile junction is often correlated to stress drops or the end of a stress drop. It is therefore suggested – at least for the sample sizes considered – that this dislocation multiplication mechanism should be take into account in continuum models such as crystal plasticity of higher order dislocation continuum theories.

Molecular Dynamics simulation are employed to investigate the structures and mechanical behavior of both symmetric and asymmetric Σ5[0 0 1] tilt grain boundaries (GBs) of copper bicrystal under uniaxial tension and shear deformation. Simulation results indicate that the Σ5 asymmetric GBs can facet into their corresponding symmetric GB structures. The maximum tensile stress of symmetric GBs is higher than the asymmetric ones at both 10 K and 300 K, which suggests the symmetric GBs may have a more stable boundary structures. All the Σ5 GBs investigate in this study can migrate under the shear deformation with different velocity. The migration of Σ5 symmetric GBs is realized by uniform displacement of local atoms and rotation of the atomic group in “E” structural unit, while for the asymmetric GBs, the migration is identified to be a diffusion-related process result from local atoms shuffling.

In the current paper we present a continuum theory of dislocations based on the second-order alignment tensor in conjunction with the classical dislocation density tensor (Kröner-Nye-tensor) and a scalar dislocation curvature measure. The second-order alignment tensor is a symmetric second order tensor characterizing the orientation distribution of dislocations in elliptic form. It is closely connected to total densities of screw and edge dislocations introduced in the literature. The scalar dislocation curvature density is a conserved quantity the integral of which represents the total number of dislocations in the system. The presented evolution equations of these dislocation density measures partly parallel earlier developed theories based on screw-edge decompositions but handle line length changes and segment reorientation consistently. We demonstrate that the presented equations allow predicting the evolution of a single dislocation loop in a non-trivial velocity field.

We discuss methods to describe the evolution of dislocation systems in terms of a limited number of continuous field variables while correctly representing the kinematics of systems of flexible and connected lines. We show that a satisfactory continuum representation may be obtained in terms of only four variables. We discuss the consequences of different approximations needed to formulate a closed set of equations for these variables and propose a benchmark problem to assess the performance of the resulting models. We demonstrate that best results are obtained by using the maximum entropy formalism to arrive at an optimal estimate for the dislocation orientation distribution based on its lowest-order angular moments.

Crystal plasticity finite element method is a useful tool to investigate the anisotropic mechanical behaviors as well as the microstructure evolution of metallic materials and it is widely used on single crystals and polycrystalline materials. However, grain boundary involved mechanisms are barely included in the polycrystalline models, and modeling the interaction between the dislocation and the grain boundaries in polycrystalline materials in a physically consisstent way is still a long-standing, unsolved problem. In our analysis, a dislocation density based crystal plasticity finite element model is proposed, and the interaction between the dislocation density and the grain boundaries is included in the model kinematically. The model is then applied to Al bicrystals under 10% compression to investigate the effects of grain boundary character, e.g. grain boundary misorientation and grain boundary normal, on the stress state and the microstructure evolution. The modeling results suggest a reasonable correspondence with the experimental result and the grain boundary character plays a crucial role in the stress concentration and dislocation patterning.