Thomas Hochrainer

A three-dimensional continuum theory of dislocation systems: kinematics and mean-field formulation

We propose a dislocation density measure which is able to account for the evolution of systems of three-dimensional curved dislocations. The definition and evolution equation of this measure arise as direct generalizations of the definition and kinematic evolution equation of the classical dislocation density tensor. The evolution of this measure allows us to determine the plastic distortion rate in a natural fashion and therefore yields a kinematically closed dislocation-based theory of plasticity. A self-consistent theory is built upon the measure which accounts for both the long-range interactions of dislocations and their short-range self-interaction which is incorporated via a line-tension approximation. A two-dimensional kinematic example illustrates the definitions and their relations to the classical theory.

Numerical implementation of a 3D continuum theory of dislocation dynamics and application to micro-bending

Crystal plasticity is governed by the motion of lattice dislocations. Although continuum theories of static dislocation assemblies date back to the 1950s, the line-like character of these defects posed serious problems for the development of a continuum theory of plasticity which is based on the averaged dynamics of dislocation systems. Only recently the geometrical problem of performing meaningful averages over systems of moving, oriented lines has been solved. Such averaging leads to the definition of a dislocation density tensor of second order along with its evolution equation. This tensor can be envisaged as the analogue of the classical dislocation density tensor in an extended space which includes the line orientation as an independent variable. In the current work, we discuss the numerical implementation of a continuum theory of dislocation evolution that is based on this dislocation density measure and apply this to some simple benchmark problems as well as to plane-strain micro-bending.

Modelling size effects using 3D density-based dislocation dynamics

We use density-based continuity equations to model strain patterns and size effects in confined plastic flow, namely, shearing of thin films and microbending. To this end, we use a representation in terms of coupled equations for the densities of screw and edge components. We show how these equations derive from a more general formulation in a higher-dimensional configuration space, and discuss relations with other density-based approaches proposed in the past. The new element here is the incorporation into previous continuum formulations of geometrical features and interactions of dislocation lines that cannot be neglected or ‘averaged out’ within a three-dimensional setting of plasticity at the micron and nano-scales.

INVESTIGATION OF SIZE-EFFECTS IN MACHINING WITH GEOMETRICALLY DEFINED CUTTING EDGES

The miniaturization of cutting processes shows process specific size-effects like the exponential increase of the specific cutting force k c with decreasing depth of cut h. Experiments were carried out in an orthogonal turning process. The influence of different process parameters on the results was investigated separately to identify process specific size-effects. Two materials were studied: a normalized steel AISI 1045 and an annealed AISI O2. To complement the experiments, parameter variations were performed in two-dimensional, thermo-mechanically coupled finite element simulations using a rate-dependent material model and analyzed by similarity mechanics. The influence of rounded cutting-edges on the chip formation process and the plastic deformation of the generated surface were determined numerically. The complex physical effects in micro-cutting were analyzed successfully by finite element simulations and compared to experiments.

Comparison of texture evolution in fcc metals predicted by various grain cluster homogenization schemes

Abstract We introduce a new material point homogenization scheme – the ‘Relaxed Grain Cluster’ (RGC) – based on a cluster of grains and formulated in the framework of finite deformations. Two variants of this scheme, which allow for different degrees of relaxation, are compared to two variants derived from the infinitesimal-strain grain interaction model regarding the evolution of texture predicted for plane-strain compression of a commercial aluminum alloy. The RGC schemes give the closest match to experimental reference on both the -fiber and the -skeleton line. The intensity of the brass texture component is found to be rather sensitive to the homogenization scheme. However, the observed decrease in texture intensity as a function of the homogenization scheme for the Cu and S component on the -skeleton line can be correlated to the number of degrees of freedom in the cluster which are left unconstrained by the respective scheme. This is in line with the significant dependence of the Cu and S component intensity on boundary conditions reported in earlier studies.

Dislocation Transport and Line Length Increase in Averaged Descriptions of Dislocations

Crystal plasticity is the result of the motion and interaction of dislocations. There is, however, still a major gap between microscopic and mesoscopic simulations and continuum crystal plasticity models. Only recently a higher dimensional dislocation density tensor was defined which overcomes some drawbacks of earlier dislocation density measures. The evolution equation for this tensor can be considered as a continuum version of dislocation dynamics. We use this evolution equation to develop evolution equations for the total dislocation density and an average curvature which together govern a faithful representation of the dislocation kinematics without having to use extra dimensions.

Similarity considerations on the simulation of turning processes of steels

Abstract In order to investigate size effects occurring in the miniaturization of turning processes a complete dimensional analysis using a materials model for high-speed deformation was performed. The derived dimensionless similarity numbers were used to guide the parameter variation in simplified two-dimensional finite-element simulations for orthogonal cutting. The rate-dependent material model leads to size effects like an increase of the specific cutting force while reducing the cutting depth. A counter-intuitive dependence of the cutting force on cutting velocity is explained using a shear-plane model. The derived dependencies on single input parameters are used to predict output values while simultaneously changing several input parameters.

Expansion of Quasi‐Discrete Dislocation Loops in the Context of a 3D Continuum Theory of Curved Dislocations

We present a numerical application of a 3D continuum theory of curved dislocations, which relies on the definition of a dislocation density in a higher order space containing orientation information. The application under consideration is the benchmark problem of a quasi‐discrete expanding dislocation loop.