Plastic-Anisotropy Modelling: Texture, Strain-Rate and Strain-Path Changes
Doctoral thesis
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http://hdl.handle.net/11250/249436Utgivelsesdato
2013Metadata
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Sammendrag
The work presented in this thesis deals with the computational modelling of the plastic anisotropy induced in the materials during the deformation process on three different scales. The main mechanism responsible for plastic deformation of aluminium at ambient temperature is the dislocation slip along certain slip systems. The specific orientations of the crystallographic directions and the slip planes with respect to the imposed deformation differentiate the slip systems to the active and passive ones. This introduces anisotropy at the microscopic scale. During the deformation, the dislocations themselves (together with particles, grain boundaries etc.) act as obstacles for the movement of other dislocations by a certain energy barrier. The dislocation–dislocation interaction is a thermally activated process of which important characteristics are the apparent activation volume and the apparent strain rate sensitivity. Correct experimental determination of these quantities, which is typically done by strain-rate change tests, is not a trivial task. The elastic-plastic transient complicates the measurement, but it can be eliminated by an advanced compensation technique. The first article contains a theoretical investigation of this issue and points on the error in the already established experimental criterion for the correct compensation, which can be up to 20% for soft tensile machines. The correct criterion is analytically derived, and based on this a guidance for the experimentalists is suggested.
As a polycrystalline material deforms to large strains, the grains have a tendency to rotate towards the stable orientations. This is due to the fact, that the dislocation slip confined to certain crystallographic planes and directions cannot by itself, without additional rotation of the whole lattice, accommodate the macroscopic deformation imposed to the material. Such individual rotations of the grains cause that the distribution of the grain orientations, i.e. the macroscopic texture of the material, is often far from random. Often a highly heterogeneous distribution of the grain orientations gives rise to a plastic anisotropy on the macroscopic scale. From the industrial point of view, it is of great importance to be able to predict, how the texture of a material will evolve during the material processing. In the second article, a new texture aggregate model is proposed. It is based on the former state-of-the-art models belonging to the group of so called 2-point models. These models are Taylor-type models, which consider pairs of two adjacent grains in a material. In order to ensure both strain compatibility and stress equilibrium between the grains, mutual relaxation of the shears components are allowed. The proposed model is compared to already existing models for the case of cold rolling of an initially random texture, as well as for an initially strong cube texture. In both cases the new model gives improved texture predictions.
The third article is a review-type of article. It serves as a comprehensive review on the classical Taylor-Bishop-Hill texture models as well as bringing new understanding of this model itself by exploring a link between the ratesensitive and rate-insensitive theories. In a way it interconnects the micro and macro scales treated in the previous two papers, since the influence of the strain rate sensitivity on the texture, r -values and the yield locus is studied. The Taylor ambiguity, i.e. non-uniqueness of the slip rates and activation of the slip systems of the rate-insensitive Taylor model is discussed with respect to the texture predictions. An improved algorithm for efficient quadratic programming is suggested and the use of the very efficient singular value decomposition, to obtain a particular solution of the Taylor ambiguity, which minimizes the sum of the square of the slip rates, is extended to the rigid plastic case. Further, it is elucidated missing physical interpretation of this particular way of solving the Taylor ambiguity of the rate-independent model by linking it to a physically based rate-dependent theory. It is argued that this link leads to a good approximation for the “cold” cases when the strain rate sensitivity is less than about 0.15. Further, the effect of an athermal resolved shear stress introduced in the viscoplastic law in the rate-dependent model is investigated and discussed based on the predictions of texture, r -values and the shape of the yield locus.
The plastic anisotropy on the macroscopic scale, due to the texture itself, cannot explain the transient changes of the flow stress and work hardening which for certain materials occur during non-proportional strain paths or when the strain path is suddenly changed. During the deformation, a heterogeneous dislocation substructure tends to develop in metals with high stacking-fault energy, consisting of regions with locally high dislocation density, e.g. dislocation walls or cell boundaries, and regions where the dislocation density is much lower, e.g. the interior of the cells or subgrains. The alignment of such substructures is associated to the imposed macroscopic deformation mode direction and is sometimes referred to as \the texture of the dislocation microstructure\. This mesoscopic scale of plastic anisotropy induced during the deformation is the subject of the fourth article. A phenomenological continuum model is proposed in order to capture both the transient and the permanent changes in the flow stress due to the strain-path changes. In the model, the presence of the built-up dislocation substructure is represented by an internal variable - a second order tensor, whose direction and magnitude reflect the directionality and the strength of the substructure, respectively. After the strain-path change, this tensor changes its direction and magnitude in the same way as the formed substructure is being rebuilt according to the actual strain path. The model was implemented as user-defined material subroutine in the finite element software LS-DYNA and tested against laboratory experiments invoking orthogonal and reverse strain path changes. The Digital Image Correlation technique was employed to observe the strain localization occurring after the orthogonal strain path change. The measured behaviour was well reproduced by the LS-DYNA simulations.