An analysis of the pile-up of infinite periodic walls of edge dislocations

We analyse the equilibrium pile-up configurations of infinite periodic walls of edge dislocations which are forced against an impenetrable obstacle by a constant applied shear stress. Numerically generated density distributions exhibit two distinct regions, for each of which we provide an interpretation and an analytical prediction. Near the obstacle, the influence of neighbouring slip planes may be neglected and the classical solution for a single slip plane applies. At a larger distance a linear decay is obtained. The characteristic length scales of the two parts of the pile-up are shown to depend differently on the parameters of the problem

On the role of dislocation conservation in higher-order crystal plasticity

The interactions between individual dislocations contribute significantly to size effects as observed at the plastic deformation of miniaturized structures. When employing a crystal plasticity framework, these interactions are usually captured by an additional balance relation. In this paper we study two approaches to capture dislocation interactions in crystal plasticity that differ by the conservation of dislocations

Computational multiscale modelling of heterogeneous material layers

A computational homogenization procedure for a material layer that possesses an underlyingheterogeneous microstructure is introduced within the framework of finite deformations.The macroscopic material properties of the material layer are obtained frommultiscale considerations. At the macro level, the layer is resolved as a cohesive interfacesituated within a continuum, and its underlying microstructure along the interface is treatedas a continuous representative volume element of given height. The scales are linkedvia homogenization with customized hybrid boundary conditions on this representativevolume element, which account for the deformation modes along the interface. A nestednumerical solution scheme is adopted to link the macro and micro scales. Numerical examplessuccessfully display the capability of the proposed approach to solve macroscopicboundary value problems with an evaluation of the constitutive properties of the materiallayer based on its micro-constitution

On the role of dislocation conservation in single-slip crystal plasticity

The objective of this paper is to evaluate the relevance of dislocation conservation within the context of dislocation-based crystal plasticity. In advanced crystal plasticity approaches, dislocations play a prominent role. Their presence, nucleation, motion, and interactions enable the explanation and description of physical phenomena such as plastic slip, hardening and size effects. While the conceptual aspects of the evolution and mechanical consequences of dislocations are treated analogously in a wide range of advanced crystal plasticity formulations, these formulations differ significantly with respect to the underlying dislocation conservation properties. This paper identifies and compares two essentially different approaches to model plastic deformations in a single crystal. Both approaches have in common that they rely on the geometrical relation between the plastic slip and the densities of geometrically necessary dislocations. In the first approach, the geometrical relation serves as a balance and is supplemented with an evolution law for the statistically stored dislocations. In the second approach the local conservation of the total number of dislocations is enforced in addition to the first balance instead of the evolution. Considering a single-slip model pile-up problem, the two representative frameworks are elaborated and confronted theoretically and numerically on the basis of a dimensionless finite-element analysis to evaluate the intrinsic role of dislocation conservation for model predictions

Deriving Global Material Properties of a Microscopically Heterogeneous Medium - Computational Homogenisation and Opportunities in Visualisation

In order to derive the overall mechanical response of a microscopically material body, both the theoretical and the numerical framework of multi scale consideration coined as computational homogenisation is presented. Instead of resolving the actual heterogeneous microstructure in all detail for its simulation, representative micro elements are considered which provide the material properties for the coarse or rather scale. This procedure allows for a smaller and less inexpensive computation. However both the chance and challenge of visualising the decisive features arise on two scales

A Computational Homogenisation Approach for Cohesive Interfaces

In this study, we introduce a homogenisation procedure for a cohesive interface between two bulk materials with an underlying microstructure determining the macroscopic response. The discontinuity is solved by an interface element and the underlying microstructure is considered as a micromophic continuum. A multiscale analysis is performed to obtain the macroscropic material properties

A Computational Homogenisation Approach for Cohesive Interfaces

In this study, we introduce a homogenisation procedure for a cohesive interface between two bulk materials with an underlying microstructure determining the macroscopic response. The discontinuity is solved by an interface element and the underlying microstructure is considered as a micromophic continuum. A multiscale analysis is performed to obtain the macroscropic material properties

Computational homogenization of material layers with micromorphic mesostructure

In this paper, a multiscale approach to capture the behavior of material layers that possess a micromorphic mesostructure is presented. To this end, we seek to obtain a macroscopic traction-separation law based on the underlying meso and microstructure. At the macro level, a cohesive interface description is used, whereas the underlying mesostructure is resolved as a micromorphic representative volume element. The micromorphic continuum theory is particularly well-suited to account for higher-order and size-dependent effects in the material layer. On considering the height of the material layer, quantities at different scales are related through averaging theorems and the Hill condition. An admissible scale-transition is guaranteed via the adoption of customized boundary conditions, which account for the deformation modes in the interface. On the basis of this theoretical framework, computational homogenization is embedded within a finite-element approach, and the capabilities of the model are demonstrated through numerical examples