Katrin Schulz

Bio: Katrin Schulz is an academic researcher from Karlsruhe Institute of Technology. The author has contributed to research in topics: Dislocation & Finite element method. The author has an hindex of 11, co-authored 35 publications receiving 246 citations. Previous affiliations of Katrin Schulz include Karlsruhe University of Applied Sciences & Applied Materials.

Analysis of dislocation pile-ups using a dislocation-based continuum theory

Abstract: The increasing demand for materials with well-defined microstructure, accompanied by the advancing miniaturization of devices, is the reason for the growing interest in physically motivated, dislocation-based continuum theories of plasticity. In recent years, various advanced continuum theories have been introduced, which are able to described the motion of straight and curved dislocation lines. The focus of this paper is the question of how to include fundamental properties of discrete dislocations during their motion and interaction in a continuum dislocation dynamics (CDD) theory. In our CDD model, we obtain elastic interaction stresses for the bundles of dislocations by a mean-field stress, which represents long-range stress components, and a short range corrective stress component, which represents the gradients of the local dislocation density. The attracting and repelling behavior of bundles of straight dislocations of the same and opposite sign are analyzed. Furthermore, considering different dislocation pile-up systems, we show that the CDD formulation can solve various fundamental problems of micro-plasticity. To obtain a mesh size independent formulation (which is a prerequisite for further application of the theory to more complex situations), we propose a discretization dependent scaling of the short range interaction stress. CDD results are compared to analytical solutions and benchmark data obtained from discrete dislocation simulations.

Dislocation multiplication in stage II deformation of fcc multi-slip single crystals

Abstract: Dislocation multiplication in plasticity research is often connected to the picture of a Frank-Read source. Although it is known that this picture is not applicable after easy glide deformation, plasticity theories often assume Frank-Read-type models for dislocation multiplication. By analyzing discrete dislocation dynamics simulations in a bulk like setting, a new view on dislocation multiplication is presented. It is observed that only two mechanisms provide a source for dislocations: cross-slip and glissile junctions. Both source mechanisms involve a change of glide system and transfer of dislocation density (line length) from the primary dislocation(s) slip system(s) to the one of the new dislocation. The motion of dislocations is found to be highly restricted by other dislocations and therefore the contribution to plastic deformation of each individual dislocation is small. Also a substantial fraction of the physical dislocation line length is annihilated by the collinear reaction, lowering dislocation storage during plastic deformation. Furthermore, multiplication events involve the loss of a substantial amount of dislocation length and curvature (sudden changes in line orientation) due to the topology changes in the dislocation network of the respective mechanisms. The findings are discussed in light of continuum dislocation theories, which currently barely account for dislocation density transfer to other systems and the limited contribution of plastic strain from individual dislocations.

Dislocation multiplication by cross-slip and glissile reaction in a dislocation based continuum formulation of crystal plasticity

Abstract: Modeling dislocation multiplication due to interaction and reactions on a mesoscopic scale is an important task for the physically meaningful description of stage II hardening in face-centered cubic crystalline materials. In recent Discrete Dislocation Dynamics simulations it is observed that dislocation multiplication is exclusively the result of mechanisms, which involve dislocation reactions between different slip systems. These findings contradict multiplication models in dislocation based continuum theories, in which density increase is related to plastic slip on the same slip system. An application of these models for the density evolution on individual slip systems results in self-replication of dislocation density. We introduce a formulation of dislocation multiplication in a dislocation based continuum formulation of plasticity derived from a mechanism-based homogenization of cross-slip and glissile reactions in three-dimensional face-centered cubic systems. As a key feature, the presented model includes the generation of dislocations based on an interplay of dislocation density on different slip systems. This particularly includes slip systems with vanishing shear stress. The results show, that the proposed dislocation multiplication formulation allows for a physically meaningful microstructural evolution without self-replication of dislocations density. The results are discussed in comparison to discrete dislocation dynamics simulations exposing the coupling of different slip systems as the central characteristic for the increase of dislocation density on active and inactive slip systems.

Big Data of Materials Science -- Critical Role of the Descriptor

Abstract: Statistical learning of materials properties or functions so far starts with a largely silent, nonchallenged step: the choice of the set of descriptive parameters (termed descriptor). However, when the scientific connection between the descriptor and the actuating mechanisms is unclear, the causality of the learned descriptor-property relation is uncertain. Thus, a trustful prediction of new promising materials, identification of anomalies, and scientific advancement are doubtful. We analyze this issue and define requirements for a suitable descriptor. For a classic example, the energy difference of zinc blende or wurtzite and rocksalt semiconductors, we demonstrate how a meaningful descriptor can be found systematically.

Mechanism-based Strain Gradient Plasticity 를 이용한 나노 인덴테이션의 해석

Abstract: Recent experiments have shown the 'size effects' in micro/nano scale. But the classical plasticity theories can not predict these size dependent deformation behaviors because their constitutive models have no characteristic material length scale. The Mechanism - based Strain Gradient(MSG) plasticity is proposed to analyze the non-uniform deformation behavior in micro/nano scale. The MSG plasticity is a multi-scale analysis connecting macro-scale deformation of the Statistically Stored Dislocation(SSD) and Geometrically Necessary Dislocation(GND) to the meso-scale deformation using the strain gradient. In this research we present a study of nano-indentation by the MSG plasticity. Using W. D. Nix and H. Gao’s model, the analytic solution(including depth dependence of hardness) is obtained for the nano indentation , and furthermore it validated by the experiments.

Atomistic simulation of tantalum nanoindentation: Effects of indenter diameter, penetration velocity, and interatomic potentials on defect mechanisms and evolution

Abstract: Nanoindentation simulations are a helpful complement to experiments. There is a dearth of nanoindentation simulations for bcc metals, partly due to the lack of computationally efficient and reliable interatomic potentials at large strains. We carry out indentation simulations for bcc tantalum using three different interatomic potentials and present the defect mechanisms responsible for the creation and expansion of the plastic deformation zone: twins are initially formed, giving rise to shear loop expansion and the formation of sequential prismatic loops. The calculated elastic constants as function of pressure as well as stacking fault energy surfaces explain the significant differences found in the defect structures generated for the three potentials investigated in this study. The simulations enable the quantification of total dislocation length and twinning fraction. The indenter velocity is varied and, as expected, the penetration depth for the first pop-in (defect emission) event shows a strain rate sensitivity m in the range of 0.037-0.055. The effect of indenter diameter on the first pop-in is discussed. A new intrinsic length-scale model is presented based on the profile of the residual indentation and geometrically necessary dislocation theory.

Automated basin delineation from digital elevation models using mathermatical morphology

Abstract: Abstract Basin delineation is a major preliminary of hydrologic modeling and watershed management. An efficient method to delineate topographic basins from digital elevation models is presented. It is based upon mathematical morphology and it consists of two major steps. First, remove all the pits within the model by using an original morphological mapping, and second, delineate topographic basins by using morphological thinnings with specific structuring elements. The results are consistent with real terrain features. In a more general way, the proposed methodology illustrates the segmentation approach provided by the morphological watershed mapping.